Séminaire Giovanni Pisante

Jeudi 15 Septembre 2011 (14h00)

Giovanni Pisante, Seconde Université de Naples.

Titre : A shape optimization problem for the nonlinear twisted Dirichlet eigenvalue.

Résumé : Aim of the talk is to discuss a recent work on a generalization of the functional defining the first twisted eigenvalue. Indeed we look at the set functional

λp,q(Ω)=inf{vLp(Ω)vLq(Ω), v0, vW1,p0(Ω), Ω|v|q2v=0}

and, under suitable conditions on p and q that ensure the existence of a minimizer function, we investigate the validity of an isoperimetric type inequality of the Reyleigh-Faber-Krahn type.
More precisely, using an alternative approach, we extend a result proved by P. Freitas and A. Henrot in the case p=q=2, proving that λp,q(Ω) is minimized by the union of two equal balls.
This talk is based on a joint work with G. Croce and A. Henrot .