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Seminari di Equazioni Differenziali e Applicazioni: Semilinear elliptic equations in convex domains and convex rings

Mercoledì 22 Gennaio 2014, ore 12:00 - Aula 1BC45 - Francois Hamel

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Mercoledì 22 Gennaio 2014 alle ore 12:00 in aula 1BC45, Francois Hamel (Université d'Aix-Marseille) terrà un seminario dal titolo "Semilinear elliptic equations in convex domains and convex rings".

Abstract
In this talk, I will discuss some geometrical properties of positive solutions of semilinear elliptic equations in bounded convex domains or convex rings, with Dirichlet-type boundary conditions. A solution is called quasiconcave if its superlevel sets are convex. I will present two counterexamples, that is two cases of semilinear elliptic equations for which the solutions are not quasiconcave.
This talk is based on a joint work with N. Nadirashvili and Y. Sire.

Rif. Int. M. Bardi, C. Marchi, L. Rossi

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