Archiv: Oberseminar Funktionalanalysis und partielle Differentialgleichungen (2014 - 2024)
12. Dezember 2024 Matteo Talluri (Univ. Bologna/Italien)
Titel: A Nonlocal Semilinear Neumann Problem and Applications to a
Chemotaxis System
Abstract: In this seminar, we will explore a fractional version of a
semilinear Neumann problem studied by Lin–Ni–Takagi
in the late 1980s.
The problem arises when the steady states of the Keller–Segel model are
considered with nonlocal
chemical concentration diffusion. There are different possible notions
of "non-local Neumann conditions" in the fractional
setting. We will
study the system both with spectral conditions, as was done by Stinga
and Volzone, and
integral conditions (introduced by Dipierro, Ros-Oton, and Valdinoci) as
was done by Cinti and Colasuonno.
While for the spectral boundary
condition there exists an extension theorem analogous to that of
Caffarelli
and Silvestre, such a theorem does not exist for integral
boundary conditions.
This makes it more difficult to obtain Liouville-type theorems and to
show that the system has non-trivial positive solutions
if the
concentration parameter is big enough.
14. November 2024 Robert Poppe (Vortrag zur Masterarbeit)
Titel: Gleichmäßige Holomorphe Störungstheorie
einfacher Eigenwerte von selbstadjungierten
Operatoren
Abstract: Dieser Vortrag befasst sich mit der holomorphen
Störungstheorie von Eigenwerten.
Dabei wird untersucht, wie sich
Eigenwerte unter holomorphen Störungen eines linearen Operators
verändern.Nach einer kurzen Einführung in die Störungstheorie, in der
wir unter anderem das
Theorem von Kato beweisen, werde ich mein
Hauptergebnis vorstellen: ein Kriterium,
das die gleichmäßige
Fortsetzbarkeit unendlicher Eigenwertsysteme ermöglicht.
12. Juli 2024 Florian Grube (Univ. Bielefeld)
Titel: EXTERIOR VALUE PROBLEMS FOR INTEGRO-DIFFERENTIAL OPERATORS
Abstract. In this talk, we discuss two results on exterior value prob-
lems for integro-differential operators. In the first part, we study a
variational setup to Dirichlet problems involving nonlocal operators like
the fractional p-Laplacian in bounded domains. In particular, we answer
the question for which exterior data weak solutions in an appropriate
Sobolev-like function space exist. This entails appropriate trace and ex-
tension theorems, see [GK23]. The fractional p-Laplacian converges to
a classical differential operator as the order of differentiation increases
to two. This phenomenon will be of particular interest to us. In the
second part of the talk, we discuss existence, uniqueness, and regularity
of distributional solutions to linear exterior-value problems involving 2s-
stable operators with square integrable exterior data. As we will have
seen in the first part of the talk, these data are too irregular for the
corresponding Dirichlet problem to be solved with variational methods.
The second part is based on the article [GHS24].
16. Mai 2024 Firoj Sk (Universität Oldenburg)
Titel: On Morrey's inequality in fractional Sobolev spaces.
i) when N, p are fixed with N<p, and s go to N/p,
ii) when s, N are fixed, and p tends to infinity,
iii) when N, p are fixed with N<p, and s goes to 1.
We further demonstrate the convergence of extremals as s goes to 1, which ensures the consistency of the well-known local results by Hynd and Seuffert. This talk is based on joint works with L. Brasco and F. Prinari.d F. Prinari.
02. Mai 2024 Nicolai Rothe (TU Berlin)
Title: Modelling of the (integer) quantum Hall effect and the Hofstadter butterfly
Abstract:
After a short introduction on the experimental setup for the classical
Hall effect and the Quantum Hall effect (QHE), I will present an
overview of the mathematical modelling of crystals, the Bloch theorem
and the Bloch-Floquet transformation. The latter transformation allows
to decompose the underlying Hilbert space into a sum of section spaces
in a corresponding family of complex line bundles. In the end, it's the
Chern numbers of these bundles, well known to be integers, which
determine the quantized Hall conductivity of a probe. Hence, a graphical
representation of of these Chern numbers in dependency of the external
magnetic field, called the Hofstadter butterfly, may be viewed as a
phase diagram for the QHE. If the time allows, I will head to some
properties of that phase diagram, e.g. its self similarity, which I had
worked on in the context of my master thesis.
Sondertermin! - Raum 901
16. April 2024 Dr. Guy Fabrice Foghem (TU Dresden)
Titel: Stability of complement value problems for p-Lévy operators.
Abstract: We
study the well-posedness of nonlocal nonlinear complement value
problems on domains governed by symmetric nonlinear integrodifferential
$p$-Lévy operators. A prototypical example of integrodifferential
$p$-Lévy operators is the well-known fractional $p$-Laplace operator
$(-\Delta)^s_p$. Asymptotically, we show that the local nonlinear
Dirichlet and Neumann boundary value problems associated with
$p$-Laplacian $-\Delta_p$ are strong limits of the nonlocal ones. We
reach this conclusion by establishing important results such as robust
Poincaré type inequalities and Gamma convergence of the nonlocal
nonlinear energies forms involved to the local ones.
18. April 2024
14:00 Uhr, Raum 110 Marius Kriegel (Frankfurt, Vortrag zur Masterarbeit)
Titel: Monotonie-basierte Regularisierung für die Rekonstruktion von schichtweise konstanten Leitfähigkeiten in der elektrischen Impedanztomographie
Abstract: In diesem Vortrag betrachten wir das inverse Problem der elektrischen Impedanztomographie für eine Klasse stückweise konstanter Leitfähigkeiten. Wir werden sehen, dass es mathematisch möglich ist diese Leitfähigkeiten unter vollständiger Kenntnis des Neumann-to-Dirichlet-Operators sowie bestimmten Annahmen exakt zu rekonstruieren. Da dieser Operator auf unendlichdimensionalen Räumen definiert ist und damit ungeeignet für die Benutzung in computergestützten Rechnungen, betrachten wir eine endlichdimensionale Approximation und leiten eine Fehlerabschätzung ab. Im Anschluss untersuchen wir die Resultate des Rekonstruktionsalgorithmus und diskutieren die Auswirkungen der Approximation auf die Ergebnisse.
Vorträge im Wintersemester 2023/2024
29. Februar 2024 Simone Dovetta (Turin)
Title: Symmetry breaking in two–dimensional square grids: persistence and failure of the dimensional crossover.
Abstract: The talk overviews some recent results about functional inequalities and nonlinear dynamics on grids. On the one hand, we consider the infinite two–dimensional square grid and we illustrate the emergence of the so–called dimensional crossover. Such a phenomenon has two evidences: the coexistence of the one and the two–dimensional Sobolev inequalities and the appearance of a continuum of L^2–critical exponents for the ground states at fixed mass of the nonlinear Schrödinger equation. On the other hand, we discuss the model robustness with respect to symmetry breaking due to the presence of defects in the grid, that is, lacks of finitely or infinitely many edges. Precisely, we begin to describe how these topological perturbations of the square grid affect the dimensional crossover, both from the standpoint of Sobolev inequalities and from that of nonlinear Schrödinger ground states. These are joint works with Riccardo Adami, Enrico Serra, Lorenzo Tentarelli and Paolo Tilli.
08. Februar 2024 Tatjana Eisner (Leipzig)
Titel: Weighted Ergodic Theorems
Abstract: We present an overview on good weights for the pointwise ergodic theorem.
01. Februar 2024
14:00 Uhr, Raum 110 Seyfullah Erkmen (Frankfurt, Vortrag zur Masterarbeit)
Titel: Implementierung von Robin-Koeffizientenproblemen in EIDORS
15.15 Uhr, Raum 110 Yassin El Karrouchi (Frankfurt)
Titel: The universal failure of the pointwise fractional Talenti comparison principle
13. Juli 2023
14:15 Uhr Huyuan Chen (Jiangxi, China)
Titel: On a nonlocal MEMS equations with variable dielectric permittivity
Abstract: Joint work with Feng Zhou and Dong Ye
In this talk, we study the nonlocal elliptic equation subject to the Dirichlet boundary condi-
tion. This equation models a electrostatic micro-electromechanical system (MEMS) device in
the more realistic case that the capacitance of the actuator is sensitive to the elastic membran-
ce's deformation. This MEMS equation was built by Lin-Yang in 2007. The difficulty to solve
the nonlocal elliptic equation arises from the nonlinearity, since the nonlocal factor breaks the
monotonicity and the traditional analysis fails to get the classification of solutions.
Combining the analysis of the related parabolic elliptic equation we obtain the dichotomy of
the existence for solutions of elliptic equation and by the choice of potential, we can get sufficient
conditions for the pull in voltage. Inversely, the results of elliptic equations is helpful to obtain
the qualitative properties of solutions parabolic problem
15:15 Uhr Alberto Saldana (Coyoacán, México)
Title: From competing species to nodal solutions of the Yamabe problem.
Abstract: What is the relationship between several populations fighting for resources and the Poincaré conjecture?
These two concepts seem to have nothing in common, but in this talk we will establish a close link by
relating three mathematical objects: the Yamabe equation, competitive systems
(that model the interaction between two species), and optimal partitions of the sphere.
This is joint work with Mónica Clapp and Andrzej Szulkin.
1. Juni 2023 Vitali Vougalter (Univ. Toronto)
Title: On the solvability of some systems of
integro-differential equations with concentrated sources
Abstract: The article is devoted to the existence of solutions
of a system of integro-differential equations in the case of the normal
diffusion and the influx/efflux terms proportional to the Dirac delta
function. The proof of the existence of solutions relies on a fixed point
technique. We use the solvability conditions for the non-Fredholm elliptic
operators in unbounded domains.
25. Mai 2023 Xueqin Peng (Gießen)
Title: Semiclassical problem for the logarithmic Schrödinger-Poisson-system
Abstract: I will discuss the Schrödinger-Poisson system with logarithmic nonlinearity and a local condition on the potential function.
The energy functional in this system is not well-defined in usual Sobolev space due to the logarithmic term. To address this,
I use a decomposition technique to express the original functional as a sum of a lower semicontinuous convex functional
and a C^1 functional. However, the lack of compactness still poses a challenge. To overcome this issue, I adapt the penalization
method proposed by M. Del Pino and P.L. Felmer to introduce a modified problem. By applying functional analytical methods,
I obtain the solution to the original problem.
This talk is based on the research results due to Alves and de Morais Filho: Z. Angew. Math. Phys. (2018).
27.04.2023 Daniel Hauer (University of Sydney)
Title: Functional Calculus via the extension technique: a first hitting time approach
13.04.2023 Sarah Kistner (Frankfurt)
Titel: Existence and Stability of Shrinkers for the Harmonic Map Heat Flow in Higher Dimensions
Abstract: A broad topic in geometrical analysis and partial differential equations is the study of harmonic maps
between Riemannian manifolds. A well-known tool in this subject is to consider the associated harmonic map heat flow.
As we are interested in blow-up mechanisms we construct for each d ≥ 4 a compact, d-dimensional, rotationally
symmetric target manifold that allows for the existence of a corotational self-similar shrinking solution that represents
a stable blowup mechanism for the corresponding Cauchy problem.
By this we expand the known results on stable self-similar blow-up for the harmonic map heat flow in the supercritical case.
The only known result apart from ours describes this phenomenon for the target being the three-sphere.
This is joint work with Birgit Schörkhuber and Irfan Glogić.
09. März 2023 Matteo Rizzi (Universität Gießen)
Title: Rigidity results for semilinear elliptic PDEs.
Abstract: In the talk I will present some classification results for solutions to semilinear elliptic equations of the form $\Delta u=W'(u)$, where $W$ is a quite general potential with a local maximum and a local minimum. We are particularly interested in proving radial symmetry of a given solution and Liouville-type Theorems, which generalise some facts which are known to be true for the Cahn-Hilliard equation. It is a joint work with Panayotis Smyrnelis (from Athens University).
15.15 Uhr Ludwig Striet (Freiburg)
Title: Approximation of fractional Operators and fractional PDEs using a sinc-basis
Abstract: We introduce a spectral method to approximate PDEs involving the fractional Laplacian with zero exterior condition. Our approach is based on interpolation by tensor products of sinc-functions, which combine a simple representation in Fourier-space with fast enough decay to suitably approximate the bounded support of solutions to the Dirichlet problem. This yields a numerical complexity of O(N log N) for the application of the operator to a discretization with N degrees of freedom. Iterative methods can then be employed to solve the fractional partial differential equations with exterior Dirichlet condition. We show a number of example applications and establish rates of convergence that are in line with rates for finite element based approaches. Further, we discuss how the provided strategies can be easily adapted to approximate other operators as well as long es they have a suitable representation as a Fourier multiplier. This includes in particular the logarithmic Laplacian
Ignace Aristide Minlend (Frankfurt)
Titel: Free boundary value problems and nonlocal partial differential equation
Di, 20.9.2022, 14 ct Raum 903 (Sondertermin!)
Silvia Cingolani (Universität Bari)
title: The effect of a potential well's topology on a fractional NLS equation
Montag, den 05.09.2022, um 15 Uhr st im Raum 903
Thomas Bartsch (Universität Giessen)
21. Juli 2022, 11:00 Uhr (s.t.) im Raum 903
Alberto Saldana (Mexico-City)
Titel: The role of the logarithmic Laplacian in the asymptotic analysis of fractional problems.
Abstract: Fractional derivatives are commonly used to model a variety of phenomena, but...
what does it mean to have a logarithmic derivative? And what would it be used for?
In this talk we focus on the logarithmic Laplacian, a pseudodifferential operator that appears
as a first order expansion of the fractional Laplacian as the exponent s goes to zero. This
operator can also be represented as an integrodifferential operator with a zero order kernel.
We will discuss how the logarithmic Laplacian can be used to study the behavior of linear and
nonlinear fractional problems in the small order limit. This analysis will also reveal a deep and
interesting mathematical structure behind the set of solutions of Dirichlet logarithmic problems.
14. Juli 2022
Jing Wu (Universidad de Granada)
Title: Overdetermined elliptic problems in onduloid-type domains with general nonlinearities.
Abstract: In this paper we prove the existence of solutions to a general semilinear elliptic problem with overdetermined
boundary conditions. The proof uses a local bifurcation argument from the straight cylinder, in analogy with the onduloids
and the theory of Constant Mean Curvature surfaces. Such examples have been found already for linear problems or with
nonlinearity f(u)=1. In this work we are able to extend this phenomenon for a large class of functions f(u).
02. Juni 2022
Antonio Greco (University of Cagliari)
Titel: Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains
Abstract: We consider semilinear PDEs in a sector-like domain. Using cylindrical coordinates (r,θ,z), we investigate the shape of solutions whose derivative in θ vanishes at the boundary. Assuming that the non-linearity f(r,z,u) is convex in u and does not depend on θ, we prove that any solution with Morse index less than two must be either independent of θ or strictly monotone with respect to θ. In the special case of a planar domain, the result holds in a circular sector as well as in an annular, and it can also be extended to a rectangular domain. The corresponding problem in higher dimensions is also considered, as well as an extension to unbounded domains. The proof is based on a rotating-plane argument: a convenient manifold is introduced in order to avoid overlapping the domain with its reflected image in the case when its opening is larger than π (joint work with Francesca Gladiali on arXiv:2201.11988).
27.5.2021, 14:15 Uhr Paolo Luzzini (EPFL Lausanne) - Videovortrag
TITLE: Asymptotics of buckling eigenvalues
ABSTRACT: Since the seminal works of Hermann Weyl at the beginning of 19th century, several authors have investigated the spectral asymptotics of partial differential operators. Following this tradition, in this talk I will first present a recent result on the Weyl's law for the buckling eigenvalues on a wide class of domains, that includes bounded Lipschitz domains. The proof does not make use of microlocal analysis and relies on asymptotically sharp lower and upper bounds that we develop for Riesz means. Moreover, we compute the second term in Weyl's law in the case of balls and bounded intervals. This, together with some formal considerations, leads us to state a conjecture for the second term in general domains. The talk is based on a joint work with Davide Buoso (UPO), Luigi Provenzano (Sapienza Università di Roma), and Joachim Stubbe (EPFL).
29.4.2021 um 15:15 Uhr (abweichende Uhrzeit!)
Omar Cabrera Chávez (Frankfurt) - Videovotrag
Title: Multiple solutions to weakly coupled supercritical
elliptic systems
04.03.3021 14 Uhr (ct): Videovortrag Yassin El Karrouchi (Frankfurt)
Titel: Einführung in die Stochastische Fluid-Dynamik: Stochastische Navier-Stokes-Gleichung
Abstract: Die Navier-Stokes-Gleichung, ein System von partiellen Differentialgleichungen deren Lösbarkeit und Regularität zu einer der Milleniumsprobleme gehört, beschreibt jegliches Verhalten von newtonschen Fluiden. Es ist klar, dass Moleküle einer Brownschen Bewegung folgen. Dies ist ein zentraler stochastische Prozess, mit dem wir eine stochastische Formulierung obiger Gleichung erhalten. Leider steht die Existenz einer Lösung der deterministischen Gleichung noch offen und damit auch die der stochastischen Navier-Stokes Gleichung. Diese Arbeit befasst sich mit der Untersuchung einer endlichdimensionalen Charakterisierung der Gleichung. Dazu wird eine stochastische Differentialgleichung betrachtet, dessen Existenz und Regularität von Lösungen zugänglicher sind und für wachsende Dimension untersucht. Hauptaussagen, werden Lösbarkeit und Regularität der endlichdimensionalen Charakterisierung sein und weitere dynamische Aspekte hinsichtlich Existenz invarianter Maße.
24.09.2020 Leon von Essen (Frankfurt)
Titel: Spektraltheorie diskreter Schrödinger- und Jacobioperatoren mit beschränkten reellwertigen Potentialen
28.07. um 16:15 Uhr Felix Höfer (Videovortrag)
Titel: "Shape derivatives for minima of integral functions"
Abstract: In this talk we will first establish a definition for the shape derivative for a certain type of integral functions under Dirichlet- and Neumann-boundary conditions. It will be shown that the shape derivative exists under fairly weak assumptions on the corresponding functions. Since by default the shape derivative is not linear in the deformation component, we achieve this by imposing some more assumptions. In this case the shape derivative can be recast as a boundary integral. The main tools used to do this are convex analysis and an application of gamma-convergence.
25.06.2020 14 Uhr ct (Videovortrag)
Joel Kübler (Frankfurt)
Title: Symmetry breaking for rotating solutions of nonlinear Klein-Gordon equations
Abstract: We study solutions of nonlinear Klein-Gordon equations with power-type nonlinearities, whose time-dependence is characterized by a rotation. This leads to a velocity-dependent elliptic equation where, in order to produce genuine rotating solutions, we investigate the existence of nonradial ground state solutions. We show that, for suitable values of the exponent in the nonlinearity, symmetry breaking occurs in the sense that the ground states transition from radial to nonradial when the velocity is varied. This is based on new degenerate Sobolev inequalities in the disc and half space with a new critical exponent. Finally, using concentration-compactness arguments, we show that the latter inequality possesses optimizers.
This is a joint work with Tobias Weth.
18.06.2020 14 Uhr ct (Videovortrag)
Lea Ebrahimi (Vortrag zur Masterarbeit)
Titel: Die Mathematik der Pauke.
Abstract: Dieser Vortrag wird sich damit beschäftigen, die Eigenmoden und -frequenzen einer Paukenmembran unter Berücksichtigung des Luftdrucks analytisch herzuleiten. Dazu wird die Pauke als Zylinder modelliert, die Membran in eine unendliche Schallwand eingebettet und äußere Raumakustik vernachlässigt. Dann soll sowohl der Druck außerhalb als auch innerhalb der Pauke die dreidimensionale Helmholtzgleichung unter Neumann-Randbedingungen erfüllen. Der Luftdruck im Inneren des Kessels wird als Greenfunktion nach Eigenfunktionen (Besselfunktionen) entwickelt. Der Luftdruck außerhalb der Pauke wird mithilfe von Greenfunktionen nach der Spiegelmethode konstruiert. Insgesamt kann so eine Gleichung an die Eigenmoden unter Luftdruck aufgestellt werden, deren Lösung nach den Eigenmoden im Vakuum entwickelt wird. Die Koeffizienten dieser Entwicklung bilden ein nicht eindeutig lösbares unendliches Gleichungssystem, das es numerisch zu lösen gilt
28.5.2020, 14 Uhr ct (Videovortrag)
Nicola Abatangelo (Frankfurt)
Title: Fractional Laplacians on ellipses
Abstract: We will illustrate some very recent findings concerning explicit evaluations of (higher-order) fractional Laplacians on elliptic domains. This will enable us to give the explicit expression of the torsion function and to construct elementary counterexamples to maximum principles. All the results have been obtained in collaboration with S. Jarohs and A. Saldana.
23.04.2020 Tolga Yesil (Frankfurt) - Videovortrag
Title: Weighted Fourier-extension estimates for symmetric functions and an application to a nonlinear Helmholtz equation.
Abstract: In this talk we present a weighted Fourier-extension estimate for symmetric functions that are nonradial.
As an application we will prove the existence of nonradial solutions for a nonlinear Helmholtz equation for
values below the Stein-Tomas critical exponent 2(N+1)/(N-1). This is a joint work with Tobias Weth"
30.01.2020 14 Uhr ct Inka Schnieders (Köln)
Titel: Ein Maximumprinzip für ein Dirichlet-Problem vierter Ordnung
23.01.2020 14:00 Uhr Babak Maboudi
Title: Detecting Jumps in a Jump-Discontinuous Random Field with Deep Neural Networks
Abstract: Random fields are important tools in mathematical modeling which help us include our lack of knowledge or our faulty measurements into scientific computing. Such fields appear frequently as parameters in many modern physics and engineering applications. When these fields are not continuous, statistical analysis and approximation of these models become more involved. In this report, we investigate detecting jump-discontinuities in the diffusion-coefficient of an elliptic stochastic partial differential equation. This is formulated as an inverse problem. We take a Bayesian approach to formulate the distribution of the jumps in the random field. We then use a Markov chain Monte Carlo (MCMC) method to explore this distribution. Common MCMC methods provide a slow convergence rate which makes solving the forward problem inefficient. We propose replacing the forward model with a feed-forward fully-connected deep neural network. This dramatically reduces computational costs while providing an accurate forward model estimation. The accuracy and the performance of the method, as well as the implication of using a neural network as a surrogate model, will be discussed.
Sondertermin Fr. 20.09.2019
14:15 Pierre Aime Feulefack (Goethe Univ. Frankfurt)
Titel: A characterization of the eigenvalues and eigenfunctions of the
logarithmic Laplacian
Abstract: In this talk, we present a new insight into the characterization
of the eigenvalues and eigenfunctions of the logarithmic
Laplacianand a new technique (delta-decomposition) to obtain the
regularity bound of eigenfunctions.
The fractional Laplacianand its corresponding eigenvalues and
eigenfunctions is the cornerstone of our study.
As an application of our results, using the delta-decomposition
technique, we prove a uniform regularity bound of eigenfunctions
of the fractional Laplacian.
15:15 Sidy Moctar Djitte (Goethe Univ. Frankfurt)
Title: NONLOCAL HADAMARD FORMULA AND ITS CONSEQUENCES
12.09.2019 - 2 Vorträge:
14:15: Jean Louis Woukeng (Université de Dschang, derzeit Univ. Heidelberg)
Title: A general approach to deterministic homogenization theory.
Abstract. We present a comprehensive approach to study deterministic homogenization problems beyond the classical periodic setting. The approach is based on a combination of tools arising from Banach algebras theory associated to the so-called concept of sigma-convergence which generalizes the well-known two-scale convergence method.
15:15 Remi Yvant Temgoua (Goethe Univ. Frankfurt)
Title: The Poisson Problem for the Regional Logarithmic Laplacian
22.08.2019 Sorin Olaru (Centrale Supelec, Paris)
Titel: Positive invariant sets for time-delay dynamical systems
Abstract: The aim of this talk is to discuss the set invariance concepts for linear time-delay systems. When described in discrete-time, these dynamics allow different set-invariance formulations according to the state space representation. A series of classical or novel existence conditions will be discussed in this framework. On a broader scope it will be shown that set-factorization represents a generalized framework for the characterization of these families of invariant sets. The links with the stability, robustness and applications to mode detection and constrained control design will be also mentioned.
13.06.2019 Antonio Fernandez Sanchez (Universite de Franche Comte/Frankreich)
Titel: On a class of elliptic problems with quadratic growth in the gradient
Montag, den 27.05.2019 - 2 Vorträge:
11 Uhr c.t., Raum 109c
Dr. Mousomi Bhakta
Titel: Fractional hardy equations with critical and supercritical exponents
16:30
Dr. Anup Biswas
Titel: Simple probabilistic method in the analysis of fractional Laplacian
Abstract: It is well-known that fractional Laplacian operators are the generators of symmetric
stable Lévy processes. In this talk we would see that how some simple probabilistic techniques
could be used to answer questions that are not really probabilistic in nature.
In particular, we would consider a generalization of the Lieb's inequality for
eigenvalues of fractional Laplacian and Liouville type results for systems of equations
involving fractional Laplacian.
12.02.2019
14:00 - 16:00 Takashi Furuya
Title: A modification of the factorization method for scatterers with different physical properties
Abstract: We study an inverse acoustic scattering problem by the Factoriza- tion Method when the unknown scatterer consists of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each object has the different boundary condition, and the other one is when different penetrability. Our idea here is to modify the far field operator depending on the cases to avoid unnecessary a priori assumptions.
07.02.2019
14:00 Uhr Olga Bondarev
Titel: Finanzmathematische Behandlung von Contingent Convertible Bonds
Abstract: In diesem Vortrag setzten wir uns zunächst mit der Funktionsweise und den preistreibenden Risiken von Contingent Convertible (CoCo) Bonds auseinander. Auf dieser Grundlage stellen wir ein Modell für den Preis von CoCo Bonds auf, dass das Volatilitäts-Smile und das Kreditrisiko berücksichtigt. Das Grundgerüst für dieses Modell bildet das Equity Derivatives Modell von J. De Spiegeleer und W. Schoutens, welches den CoCo Bond in eine Anleihe und Barriere-Optionen zerlegt. Die Modellparameter kalibrieren wir an Marktpreise von Plain-Vanilla Optionen und an CDS Quotierungen. Den Preis nähern wir mit einem Monte-Carlo-Verfahren ergänzt um die Brownsche Brücke an und untersuchen an einem Beispiel die Konvergenz dieses Verfahrens.
15:15 Uhr Julian Fels
Titel: Particle Swarm Optimization
Abstract: Particle Swarm Optimization oder Partikelschwarmoptimierung ist ein globales, schwarmbasiertes Optimierungsverfahren, das im weiten Sinne zum Bereich der künstlichen Intelligenz gezählt wird. Inspiriert durch das natürliche Schwarmverhalten von Vögeln durchsuchen Individuen ein großes Suchgebiet in Abhängigkeit sowohl der eigenen besten Position als auch der besten Position der anderen Schwarmmitglieder. Angewandt auf restringierte Optimierungsprobleme erzielt diese Methode vielversprechende Ergebnisse. Die vorliegende Arbeit dient als Einführung in die Funktionsweise des Algorithmus und bietet einen Überblick über den aktuellen Forschungsstand in diesem Gebiet. Ein Fokus dieser Arbeit liegt dabei auf der einfachen Implementierung in MATLAB und dem breitgefächerten Einsatzgebiet des Algorithmus. Neben restringierten Optimierungsproblemen wird auch in die Anwendung des Algorithmus auf dem Gebiet der Clusteranalyse eingeführt. Als Ausblick auf zukünftige Forschungen soll zusätzlich ein Einblick in die Programmierung auf Grafikkarten mit MATLAB und CUDA gegeben werden. Dazu wird die grundlegende Architektur der GPU-Programmierung erläutert und Kriterien für eine sinnvollen Einsatz herausgearbeitet. Das hohe Potential der parallelen Implementierung und weitere Erkenntnisse dieser Arbeit werden abschließend durch eine experimentelle Analyse gestützt.
14:00 - 16:00 Dr. Martin Simon (Head of Equity and Equity Derivatives Valuation, Deka Investment GmbH)
Titel: "Aktienpreisblasen - Ein Indikator auf Basis börsengehandelter Optionen"
Abstract: In diesem Vortrag diskutieren wir einen mathematischen Indikator für Aktienpreisblasen. Der erste Teil hat einführenden Charakter und fasst die Theorie strikter lokaler Martingale zur Modellierung von Preisblasen sowie die Implikationen für die Bewertung derivativer Finanzinstrumente zusammen. Im zweiten Teil wird ein neuartiger, vorwärts blickender Indikator vorgestellt, welcher den Informationsgehalt von Geld- und Briefkursen börsengehandelter Plain Vanilla Optionen verwendet. Diese Konstruktion ist motiviert durch ein neues theoretisches Resultat von A. Jacquier and M. Keller-Ressel, welches zeigt dass Preisblasen anhand des asymptotischen Verhaltens der impliziten Volatilitätsfläche identifiziert werden können. In der Praxis führt dies auf ein schlecht-gestelltes inverses Parameteridentifikationsproblem; wir schlagen einen statistischen Ansatz vor, um die daraus resultierende Unsicherheit zu quantifizieren. Im dritten Teil des Vortrags werden reale Beispiele präsentiert welche sich mit der aktuell viel diskutierten Sorge vor einer Tech Blase 2.0 befassen.
01.11.2018 - zwei Vorträge
14:00 Uhr Hugo Tavares (Lissabon/Portugal)
Title: Variational Problems with long-range interactions
Abstract: In this talk we consider a class of variational shape optimisation problems for densities
that repel each other at a certain distance. Typical examples are given by the Dirichlet functional
and the Rayleigh functional minimised in the class of functions that attain some H^1 boundary
conditions, subject to the constraint that the supports of different densities are at distance at least one.
For these problems, we show a connection with solutions to variational elliptic systems with nonlocal
competing interactions, we investigate the optimal regularity of the solutions, prove a free-boundary
condition, and derive some preliminary results characterising the free boundary. This is a joint work
with N. Soave, S. Terracini and A. Zilio
15:15 Uhr Johannes Wagner (Frankfurt)
Titel: "Extrapolation für Runge-Kutta-Verfahren"
Abstract: In der Numerik gewöhnlicher Differentialgleichungen spielen Einschrittverfahren eine
zentrale Rolle. Verfahren höherer Konvergenzordnung liefern in der Praxis einen kleineren
Gesamtfehler, mithilfe von Extrapolation kann diese erhöht werden. Wir geben eine Konstruktion
von Runge-Kutta-Verfahren beliebig hoher Ordnung an und untersuchen die konstruierten
Verfahren auf ihre Stabilitätseigenschaften.
27.09.2018 14.15 Uhr Katharina Jung (Frankfurt)
Titel: Symmetriebrechung bei Lösungen semilinearer Dirichletprobleme
Abstract: Wir betrachten semilineare Dirichletprobleme in der Einheitskugel bzw. in einem Annulus.
Dabei untersuchen wir die Eigenschaften von Lösungen mit Vorzeichenwechsel anhand des Morse
Index und zeigen, unter welchen Bedingungen die Knotenlinie den Rand berührt. Insbesondere
zeigen wir, dass jede nodale Lösung minimaler Energie nichtradial ist und ihre Knotenlinie den Rand berührt.
30.08.2018
14:00 Ali Suri (Bu-Ali Sina University, Hamedan, zur Zeit Frankfurt)
Titel: "On the Geometry of the Symplectomorphism Group"
15:30 James Benn (University of Notre Dame, zur Zeit Frankfurt)
Titel: "Geometric Hydrodynamics and Recurrence Properties of Rossby-Hurwitz Waves"
28.06.2018 Tolga Yesil
Titel: Stein-Tomas inequality for symmetric functions
Abstract: In this talk we study the Stein-Tomas inequality for functions with specific symmetries. This inequality yields (p,q)-estimates for the so called Fourier-restriction operator, i.e. the operator that restricts the Fourier transform of an admissible function to a hypersurface in Euclidean space. By considering the sphere, we will present how additional symmetries on the corresponding functions interact with the possible range of exponents.
21.06.2018 Joel Kübler
Titel: Nonradial bifurcation for the Henon equation
Abstract: We study the nonlinear Henon equation on a ball and show that, as a parameter goes to infinity, nonradial solutions bifurcate from radial solutions. Our main tool is a thorough analysis of the eigenvalues of associated linearized operators which is based on a suitable rescaling of the equation. This allows us to identify a limit problem and yields asymptotic estimates for these eigenvalues.
14.06.2018 Rebekka Pech
Titel: Image Inpainting
Abstract: Image Inpainting ist eine bereits fest etablierte Methode in der digitalen Bildbearbeitung, um beschädigte oder entfernte Teile eines Bildes adäquat zu füllen. In dieser Arbeit werden einige diffusionsbasierte (basierend auf der Wärmeleitungsgleichung, dem Variationsansatz oder Eulers Elastica) und texturbasierte Herangehensweisen an dieses Problem studiert und anschließend hinsichtlich ihrer Effizienz miteinander verglichen.
17.05.2018 Daniel Roth
Titel: Monte Carlo pfadweise Ableitungen für Barriere Optionen
Abstract: Das pfadweise Schätzen der Ableitungen bei Monte Carlo Verfahren ist für glatte
Auszahlungsfunktionen fest etabliert. In dieser Arbeit präsentieren wir einen neuen Monte Carlo
Algorithmus, welcher die pfadweisen Ableitungen von unstetigen Funktionen berechnen kann.
Unser Ansatz besteht darin die Idee des one-step survivals von Glasserman und Staum mit der
Methode zum stabilen Ableiten von Alm, Harrach, Harrach und Keller zu verbinden.
Als Anwendung werden wir die hergeleiteten Resultate verwenden, um eine zwei-dimensionale
Kalibrierung eines Coco-Bonds durchzuführen, welchen wir mit verschiedenen Arten von,
an diskreten Zeitpunkten überwachten, Barriere Optionen modellieren.
06.04.2018, Dr. Sarah Eberle
Titel: Wave Propagation and Post-Processing
05.04.2018, Michael Ertel
Titel: Das regularisierte Halley-Verfahren zur Lösung eines inversen nichtlinearen Gravimetrie-Problems
Titel: Schauder type estimates for a class of linear partial differential equations
06.07.2017 Huyuan Chen (Nanjing University/China, z Zt. Frankfurt am Main)
Titel: Liouville theorem for fractional semilinear equations in unbounded domains
29.06.2017 Vortrag von Dr. Janosch Rieger, Monash University
Title: Recent advances in domain reconstruction from electrical impedance
tomography data
Abstract:
Electrical impedance tomography is an emerging budget-priced,
non-invasive medical imaging technique that is very likely to
complement computerised tomography in important applications
such as pulmonary function control and breast cancer screening
in the future. The main difficulty associated with this technology
is that the arising inverse problem is strongly ill-posed.
22.06.2017 Tolga Yesil (Frankfurt am Main)
Titel: Dual ground state solutions for the critical nonlinear Helmholtz equation
Abstract: Using a dual variational approach, we obtain real-valued solutions of a
weighted critical nonlinear Helmholtz equation. The weight function is
assumed to be bounded, positive, asymptotically periodic and to satisfy
a certain flatness condition at one of its maximum points. The solutions
obtained are so-called dual ground states, i.e. solutions arising from
critical points of the dual functional with the property of having
minimal energy among all nontrivial critical points. This is a joint
work with Gilles Evequoz.
Sondertermin: Dienstag, 04.04.2017, 11:00 Uhr (c.t.) in Raum 110 (RMS 10)
Vortrag von Minh Nguyet Mach, Ph.d. (University of Helsinki)
Title:"Convergence of the current-to-voltage measurements of the Shunt Electrode Model to those of the Continuum Model"
09.02.2017 Sven Jarohs (Frankfurt am Main)
Titel: Starshape of superlevel sets of solutions to equation involving the fractional Laplacian
Abstract: In this talk, I will present a general framework to analyze the geometry of solutions to equations
involving the fractional Laplacian in starshaped rings. By analyzing the difference of the solution with a scaled
version of this solution, using the scaling properties of the fractional Laplacian and different versions of
maximum principles, we show that under rather general assumptions on the right-hand side the solution
has starshaped superlevel sets. I will also present some examples in which this result can be applied.
The talk is based on a joint work with Tadeusz Kulczycki and Paolo Salani.
02.02.2017 Sebastian Becker (Goethe-Universität Frankfurt)
Titel: Nicht-autonome und zufällige dynamische Systeme, die durch deterministische und stochastische
Differentialgleichungen generiert sind (Masterarbeit)
Abstract: Im Vortrag werden autonome, nicht autonome und zufällige dynamische Systeme vorgestellt,
miteinander verglichen und erweitert. Anhand von zunächst skalaren Differentialgleichungen werden die
induzierten dynamischen Systeme mit den zuvor vorgestellten Definitionen in Verbindung gebracht, um
so den nicht autonomen Einfluss besser untersuchen zu können. Des weiteren werden gemeinsam
wirkender nicht-autonomer deterministischer und stochastischer Einfluss betrachtet und so generierte
Systeme analysiert.
19.1.2017 Oscar Agudelo (University of West Bohemia, Pilsen)
Titel: Boundary concentration phenomena for the higher-dimensional Keller-Segel system
Abstract: We study the existence of steady states to the Keller-Segel system with linear chemotactical
sensitivity function on a smooth bounded domain in RN, N ≥ 3, having rotational symmetry. We find three
different types of chemoattractant concentration which concentrate along suitable (N−2)−dimensional
minimal submanifolds of the boundary. The corresponding
density of the cellular slime molds exhibit in the limit one or more Dirac measures supported on
those boundary submanifolds.
This is a joint work with Angela Pistoia from La Sapienza, Università degli Studi di Roma.
Titel: Ground states for irregular and indefinite superlinear Schrödinger equations
Abstract: We consider the existence of a ground state for the subcritical stationary
semilinear Schrödinger equation −∆u + u = a(x)|u| p−2 u in H 1 , where a ∈
L ∞ (R N ) may change sign. Our focus is on the case where loss of compactness
occurs at the ground state energy. By providing a new variant of the Splitting
Lemma we do not need to assume the existence of a limit problem at infinity, be
it in the form of a pointwise limit for a as |x| → ∞ or of asymptotic periodicity.
That is, our problem may be irregular at infinity. In addition, we allow a to
change sign near infinity, a case that has never been treated before.
27.10.2016 Marcello di Biase (Goethe-Universität Frankfurt)
Titel: Über Stochastische Bifurkation
Abstract: Große Anstrengungen galten in den letzten Jahrzehnten den Versuchen, eine Bifurkationstheorie für zufällige dynamische Systeme zu schaffen, die als Verallgemeinerung der gut verstandenen Bifurkationsszenarien deterministischer Dynamik verstanden werden kann. Die Ergebnisse sind so vielfältig wie die Klassen der untersuchten zufälligen dynamischen Systeme selbst. Einige ausgewählte Ansätze werden umrissen, Beispiele diskutiert und auf ansatzspezifische Eigenheiten aufmerksam gemacht.
20.10.2016 Maximilian Engel (Imperial College London)
Titel: "Bifurcation analysis of stochastically driven limit cycles"
Abstract: We investigate bifurcations from an attractive random equilibrium to shear-induced chaos for stochastically driven limit cycles, indicated by a change of sign of the first Lyapunov exponent. This addresses an open problem posed by Lai-Sang Young and co-workers, extending results on periodically kicked limit cycles to the stochastic context. We also apply concepts from ergodic theory, like entropy and the SRB property of the invariant random measure, to describe the random attractors in the chaotic case.
6.10.2016 14 ct, Raum 110
Nicola Abatangelo (Brüssel)
Title: A very weak theory for fractional Dirichlet problems
Abstract: It is long since known that s-harmonic functions (namely, functions whose fractional Laplacian is zero) on a domain can show an explosive behaviour at the boundary, in sharp contrast with classical harmonic functions. We will present a theory of Stampacchia's sort for solutions to fractional elliptic Dirichlet problems which can deal with such singular behaviour. In order to gain uniqueness and, more generally, well-posedness, these boundary problems are set by prescribing two different types of Dirichlet datum at the same time, one of which is describing the asymptotic explosive profile of the solution at the boundary.
27.07.2016 11:00 Uhr st, Raum 110
Sven Jarohs (Goethe-Universität Frankfurt)
Titel: On the maximum principle for the fractional polylaplacian
Abstract: It is well-known that in general operators of order four do not satisfy
a maximum principle for supersolutions. Since maximum principles are an
important tool in the analysis of partial differential equations, the
question arises why and when this property is lost for operators of
order between 2 and 4. In this talk we will analyze real, positive
powers of the Laplacian and show that whenever the power is in an
Intervall starting with an odd number, then the maximum principle fails.
By the structure of the explicit counterexample it follows that such
powers of the fractional Laplacian may satisfy a maximum principle only
for solutions in certain connected sets. One of such sets is given by
the ball, where the maximum principle follows from an explicit solution
formula given by Boggio's formula. The talk is based on a joint work
with Nicola Abatangelo and Alberto Saldana.
14.07.2016 14 Uhr ct Rohit Kumar Mishra (Bangalore/Indien)
Titel: On Inversion of Some Integral Transforms in R^n
07.07.2016 14 Uhr c.t. Andreas Hauptmann (Universität Helsinki/Finnland)
Titel: Direct reconstructions from partial-boundary data in electrical impedance tomography
Abstrakt: In electrical impedance tomography a body is probed with an electrical
current to obtain information about the inner conductivity distribution. In this
application full-boundary measurements are not always possible. Therefore, we
present the partial-boundary inverse conductivity problem in a realistic setting
and analyze the error that partial-boundary measurements introduce. Computational
convergence results and reconstructions are presented for medical motivated simulated data.
07.07.2016, 15 Uhr c.t. Daniel Roth (Frankfurt am Main)
Titel: Monte-Carlo Verfahren für die Elektrische Impedanz-Tomografie
Abstract: Das direkte Problem der elektrischen Impedanz-Tomografie
beschäftigt sich damit, für eine bekannte Leitfähigkeit durch angelegten
Strom das zugehörige Potential zu berechnen. Dieses Problem kann
beispielsweise mit einem Finite-Differenzen Verfahren gelöst werden. Der
Vortrag widmet sich einem alternativen Verfahren zum Lösen des direkten
Problems. Dieses Verfahren, welches auf auf einem Monte-Carlo
Algorithmus basiert, löst mittels Zufallszahlen das Gleichungssystem der
Finiten Differenzen, ohne das Gleichungssystem explizit aufzustellen.
02.06.2016 14 Uhr ct Elias Polak (Frankfurt)
Titel: Die Grundzustandsenergie eines N-Fermionen-Systems (Bachelorarbeit)
04.02. 2016 Fabian Rücker (Frankfurt)
Titel: Anwendung des Minimax-Theorems von Nikaido auf Probleme der
Kontrolltheorie
Sondertermin, Mittwoch, den 03.02.2016 16-18 Uhr, Raum 404
16:15 Uhr Prof. Susanna Terracini (Turin)
Titel: Entire solutions and spiralling asymptotic profiles of competition diffusion sytems
17:15 Uhr Prof. Gianmaria Verzini (Milano)
Titel: Strong competition versus fractional diffusion
21.01.2016 Dr. Alberto Saldana (Brüssel)
Titel: On the extended Allen-Cahn equation.
Abstract: Nonlinear fourth-order PDEs usually have a richer and more complex set of solutions
when compared to its second-order counterpart. In this sense, many models exhibit behaviors
that could be better described with fourth-order equations, like ocean and atmosphere dynamics,
bridges, and pattern formation, just to mention some of them. The theory for higher-order nonlinear
problems, however, is far less developed than its second-order analogue and many basic questions
remain open. Lack of maximum principles, oscillatory behavior of solutions, and regularity issues
are some of the main difficulties in the study of such problems.
I this talk I consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and
Navier boundary conditions. I present results on existence, uniqueness, positivity, stability, a priori
estimates, and symmetry. As an application, we construction a saddle solution in the whole space.
The proofs rely on variational and bifurcation methods. Some numerical approximations of solutions
will also be discussed.
14.01.2016 Linda Lintz (Frankfurt)
Titel: Der fraktionale p-Laplace-Operator
05.11.2015 Dr. Stefanie Hollborn (Universität Mainz)
Titel: Ein schnelles Prüfverfahren der elektrischen Impedanztomographie
Abstract: Die elektrische Impedanztomographie erzeugt Bilder des unsichtbaren Körperinneren
eines Untersuchungsobjekts, indem sie die Werte der elektrischen Leitfähigkeit im Inneren aus
Strom-Spannungsmessungen an der Körperoberfläche (mathematisch) ermittelt. In vielen
Anwendungen muss diese Leitfähigkeitsverteilung allerdings nicht vollständig rekonstruiert
werden, sondern es genügt zu überprüfen, ob und wo die Leitfähigkeit von einem erwarteten
Wert abweicht. Diese Regionen - sogenannte Inhomogenitäten - weisen bei Materialprüfverfahren
beispielsweise auf Schadstellen hin.
29.10.2015 Max Weidemann (Uni Frankfurt)
Titel: Monotoner Transport von Wahrscheinlichkeitsmaßen (Bachelor-Arbeit)
22.10.2015 Friedrich Schäufele
Titel: Sequential Quadratic Programming: Theorie, Implementierung und Anwendung
15.10.2015 Thomas Varnay (Frankfurt)
Titel: Konstruktion von Frames
08.10.2015 Zhitao Zhang (Chinese Academy of Sciences, Bejing)
Beginn: 15 Uhr ct
Titel: Existence, symmetry and bifurcation of solutions for Schrödinger systems
Abstract: We are concerned with the important system of nonlinear Schrödinger equations with linear
and (or) nonlinear couplings which arises from Bose-Einstein condensates, we prove Terracini's conjecture
for the phase segregation of the limit competition case, we use variational methods and bifurcation
theory to prove the existence of ground state and bound state solutions of the systems, structure of
and the (partial) symmetry of solutions of the systems.
13.8.2015 Joel Kübler (Frankfurt)
Titel: Charakterisierung von Herglotz-Wellen
30. Juli 2015 Marcel Freitag (Univ. Paderborn)
Titel: Finite speed of propagation in a fourth-order degenerate parabolic equation modeling
Bose-Einstein condensation
7. Mai 2015 Matthias Gundlach (Technische Hochschule Mittelhessen, Gießen)
Titel: Chaos für die Raumklimatisierung
Abstract: Raumluftströmungen lassen sich mit Differenzialgleichungssystemen beschreiben, die dem
aus der Chaostheorie bekannten Lorenz-System ähneln und entsprechende Phänomene aufweisen.
Letztere können in der Klimatisierung von Räumen zur Energieeffizienzsteigerung genutzt werden.
In dem Vortrag werden die Modelle zur Beschreibung von Raumluftströmungen vorgestellt, die zugehörige
Dynamik samt ihrer Attraktoren vorgestellt und erläutert, wie diese Attraktoren für chaotische Strömungen
in Räumen auch auf der Grundlage von experimentell ermittelten Daten nachgewiesen werden können
06.02.2014 Dr. Gilles Evequoz (Frankfurt) Titel: Reelle L^p-Lösungen der nichtlinearen Helmholtz-Gleichung Abstract: Die Helmholtz-Gleichung wird u.a. zur Modellierung der Ausbreitung von akustischen Wellen verwendet. In diesem Vortrag wird zunächst ein Überblick über die Lösungstheorie im linearen Fall gegeben. Darauf aufbauend werden neue, auf variationellen Methoden beruhende Resultate über die Existenz und die Fernfeldentwicklung von reellen L^p-Lösungen im nichtlinearen Fall vorgestellt. Diese Lösungen korrespondieren zu zeitperiodischen Lösungen der zugehörigen Wellengleichung mit zeitlich konstanter Energiedichte (stehende Wellen).24. Juli 2014 Metin Tapirdamaz Titel: Hausdorff-Dimension zufälliger Attraktoren 17. Juli 2014 Anne Heppner (Frankfurt) Titel: Qualitative Analyse von Rossby-Wellen Abstract: Rossby-Wellen bezeichnen großräumige Wellenbewegungen in der Atmosphäre oder dem Ozean, die sich horizontal ausbreiten. Diese spielen eine wichtige Rolle für die Entwicklung von Hoch- und Tiefdruckgebieten. Im Vortrag wird ein mathematisches Modells auf der Grundlage partieller Differentialgleichungen hergeleitet, dessen Lösungen die Wellen beschreiben. Ferner wird ein klassisches Resultat von Kloeden über die Eindeutigkeit einer Familie antisymmetrischer Lösungen präsentiert. Der wesentliche Schritt in der Herleitung dieses Resultats ist der Beweis der radialen Symmetrie einer in meridionaler Richtung skalierten Lösung. 3. Juli 2014 Prof. Nils Ackermann (UNAM, Mexiko-Stadt) Titel: Growth estimates for Laplacian eigenvalues under partial symmetries and applications to Bahri-Lions type results Abstract: We prove new estimates for the growth of the eigenvalues of the Dirichlet Laplacian on a bounded domain that is partially symmetric. These are reminiscent of Lieb-Cwikel-Rosenbljum type results. We apply these estimates to a perturbed Lane-Emden equation on a partially symmetric bounded domain to obtain results in the Spirit of Bahri and Lions. To achieve this we use an existence result of Tanaka for critical points in a symmetric mountain pass setting with prescribed lower bounds for the Morse indices. Together with our spectral estimates these yield improved growth rates for the respective partially symmetric critical levels of the unperturbed problem. An application of Bolle's perturbation method yields the existence of an infinity of solutions for the perturbed problem under weaker conditions on the exponents than known before. 8. Mai 2014 Nikolaos Sfakianakis (Mainz) Title : "A finite element method for the simulation of motility of living cells" Mittwoch, 19.02.14, Raum 110, Prof. Jacson Simsen – UNIFEI - Brazil Titel: On global attractors for parabolic problems with variable exponents Abstract: In this talk I will give an overview on the results which we have obtained during the last 5 years about existence and upper semicontinuity of global atractors for parabolic problems with variable exponents. 06.02.2014 Dr. Gilles Evequoz (Frankfurt) Titel: Reelle L^p-Lösungen der nichtlinearen Helmholtz-Gleichung Abstract: Die Helmholtz-Gleichung wird u.a. zur Modellierung der Ausbreitung von akustischen Wellen verwendet. In diesem Vortrag wird zunächst ein Überblick über die Lösungstheorie im linearen Fall gegeben. Darauf aufbauend werden neue, auf variationellen Methoden beruhende Resultate über die Existenz und die Fernfeldentwicklung von reellen L^p-Lösungen im nichtlinearen Fall vorgestellt. Diese Lösungen korrespondieren zu zeitperiodischen Lösungen der zugehörigen Wellengleichung mit zeitlich konstanter Energiedichte (stehende Wellen).
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