12
Fachbereich
Institut für Mathematik
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Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Termin und Ort:

Donnerstags, 14 Uhr ct, Raum 711 groß, Robert-Mayer-Straße 10

Veranstalter:

Dr. Sven Jarohs
Prof. Dr. T. Weth

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Jan 22 2026
14:00

Raum 711 groß

Giulio Bartoli (Frankfurt): The Gaussian-like p-Laplacian: Dirichlet problem, eigenvalues, and the Faber–Krahn inequality

Abstract: 

The Gaussian-like p-Laplacian: Dirichlet problem,eigenvalues, and the Faber–Krahn inequality
In this thesis, we extend several classical results for the Euclidean p-Laplacian,
∆pu = div(|∇u|p−2∇u), to a setting where the Lebesgue measure is replaced by a
Gaussian-like measure dμ = Ze−W dLN . Under this measure, the operator takes
the form div(|∇u|p−2∇u) − |∇u|p−2⟨∇u, ∇W ⟩. Our study specifically focuses on
the Dirichlet problem and the associated eigenvalue problem. In particular, for the
weak Dirichlet problem, we prove existence and uniqueness of the solution. As for
the eigenvalue problem, the analysis focuses on the first eigenvalue. We show that
a Faber-Krahn inequality holds in this context as well

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Jan 15 2026
14:00

Raum 711 groß

Laura Baldelli (KIT Karlsruhe): Radial symmetry in doubly critical Hardy–Sobolev quasilinear systems 

 This talk concerns a family of Hard-Sobolev doubly critical quasilinear systems defined on the entire Euclidean space. In particular, we investigate the radial symmetry of positive solutions to such systems by employing the moving plane method. The application of this method is highly nontrivial due to the nonlinear nature of the p-Laplace operator. Moreover, adapting standard techniques encounters additional difficulties arising from the presence of the Hardy potential. To overcome these obstacles, we employ a variant of the test function method, which in turn introduces further technical challenges.

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Dez 11 2025
14:00

Raum 107

Lea Ebrahimi (Frankfurt):  On the Well-Posedness of the Stationary Quasigeostrophic Equation

The quasigeostrophic equation is a nonlinear active scalar equation //in which the velocity field is determined nonlocally from the transported scalar. It is closely related in structure to the 2D Euler equations written in vorticity form. In this talk, I will discuss its stationary version, focusing on existence and uniqueness of weak solutions.

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Dez 4 2025
14:00

​Raum 711 groß

Sven Jarohs (Frankfurt): On a class of (non)local superposition operators of arbitrary order

The superposition of operators of different order has been a general interest reaching from purely nonlocal interactions described by the sum of fractional Laplacians with different order, mixed local-nonlocal type operators or purely local operators such as the sum of the Laplacian and the bilaplacian. In this talk, I present a general variational framework, which will contain a broad class of Lévy-type operators and which will also include higher-order operators like the polylaplacian. More generally, the present framework will allow to study operators of possible infinite order. The latter will lead to a classification of measures on [0,∞) with unbounded support. The talk is based on a joined project with Serena Dipierro and Enrico Valdinoci.

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Okt 28 2025
14:00

Héctor Chang-Lara CIMAT/Mexiko):  Regularity Estimates for Zeroth Order Operators

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Okt 17 2025
11:00

Sondertermin, Raum 903

Jehan Oh (Kyungpook University/Korea): Regularity for elliptic and parabolic double phase problems 

In this talk, we investigate some regularity results for
elliptic and parabolic double phase problems. We first introduce a
double phase problem which is characterized by the fact that its
ellipticity rate and growth radically change with the position. We then
explore the optimal regularity conditions on the modulating coefficient
depending on the size of the phase transition and present related
theoretical developments. Extensions to double phase models with two
modulating coefficients, as well as multi phase problems, will also be
discussed. The latter part of the talk will be devoted to the parabolic
setting. We present recent results on regularity theory for
time-dependent double phase problems and aim to establish higher
integrability results by introducing a suitable intrinsic geometry.

Oberseminar Funktionalanalysis und partielle Differentialgleichungen

Sep 18 2025
14:15

Raum 107

Efe Akbayir (Frankfurt): Der fraktionale Laplace-Operator und die Caffarelli–Silvestre-Erweiterung - Vortrag zur Bachelorarbeit

Die Caffarelli–Silvestre-Erweiterung liefert eine Lokalisierung des fraktionalen Laplace-Operators. Dazu werden gegebene Dirichlet-Randwerte durch die Lösung einer degeneriert elliptischen Gleichung im Halbraum fortgesetzt und der fraktionale Laplace-Operator ergibt sich als Neumann-Randwert dieser Lösung. Abhängig von der Regularität der Randdaten lassen sich geeignete Funktionsräume festlegen, in denen die Erweiterung wohldefiniert und eindeutig lösbar ist.