Nonlinear PDE Days

Frankfurt - Gießen - Karlsruhe

Analytical and Computational Methods in Geometric Optimization Problems

Goethe-Universität Frankfurt, July 1 - 2, 2010

 

Speakers

Friedemann Brock (American University of Beirut)

Antoine Henrot (Ecole des Mines de Nancy)

Bernd Kawohl (Universität zu Köln)

Andrea Malchiodi (SISSA, Trieste)

Edouard Oudet (Université de Savoie)

 

Organizers

Thomas Bartsch (Universität Gießen),  Michael Plum (KIT Karlsruhe),  Wolfgang Reichel (KIT Karlsruhe),  Tobias Weth (Universität Frankfurt)

 

Location

Institut für Mathematik, Robert-Mayer-Straße 10, 60054 Frankfurt am Main, Lecture Room 711 gr.

Map

 

Schedule

Thursday, July 1^st 2010

2:00 -2:50 p.m  Andrea Malchiodi (SISSA, Trieste): Variational theory for Liouville equations on compact surfaces. Part I.

Abstract: We consider Liouville equations on compact surfaces, motivated by the study of self dual Chern-Simons models and by conformal geometry. Using suitable improvements of the Moser-Trudinger inequality and variational methods we prove generic existence results.

3:00 - 3:50 p.m.  Friedemann Brock (American University of Beirut): Symmetry of ground states for elliptic equations involving the Laplacian and power-type nonlinearities

Abstract

3:50 - 4:30 p.m.  Coffee break

4:30 - 5:20 p.m.  Antoine Henrot  (Ecole des Mines de Nancy): The Mahler conjecture and some other optimization problems with convexity constraints

Abstract: Let K be a convex body and K^o its dual body. The Mahler volume is the product of the volume of K and K^o and the Mahler conjecture states that this quantity should be minimized by the cube. It is open in dimension greater or equal to three. We will give a new proof of this conjecture in two dimensions and give some new informations about the minimizers in any dimension. We will also consider some other optimization problems among convex sets whose solutions are polygons.

Friday, July 2^nd 2010

9:00 - 9:50 am Andrea Malchiodi (SISSA, Trieste): Variational theory for Liouville equations on compact surfaces. Part II

10:00 - 10:50 a.m. Edouard Oudet (Université de Savoie): Modeling and optimization by Gamma-convergence

Abstract: We present in this talk two completely different examples of the use of \Gamma-convergence results to model and approximate geometrical objects. The first example is related to optimal tilings in 2D and 3D with respect to spectral energies. The second part adresses the problem of optimal irrigation networks approximation .

10:50 - 11:30 a.m. Coffee break

11:30 am - 12:20 p.m. Bernd Kawohl (Universität zu Köln): An isoperimetric inequality related to a Bernoulli problem

Abstract: Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in [Flucher et al., J. Reine Angew. Math. 486 (1997), 165–204.

For registration and hotel reservation, please contact Mrs Jacqueline Habash: habash@math.uni-frankfurt.de,  ++49-69-798-22511

Poster

 

geändert am 18. März 2010  E-Mail: Bürobuero@math.uni-frankfurt.de

|

| Zur Navigationshilfe