60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
De Philippis, Guido
106 Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Velichkov, Bozhidar
24474 Laboratoire Jean Kuntzmann [LJK]
Type
Article accepté pour publication ou publié
Abstract (EN)
The classical Faber–Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet Laplacian among sets with given volume. In this article we prove a sharp quantitative enhancement of this result, thus confirming a conjecture by Nadirashvili and by Bhattacharya and Weitsman. More generally, the result applies to every optimal Poincaré–Sobolev constant for the embeddings W1,20(Ω)↪Lq(Ω).
