Faber-Krahn inequalities in sharp quantitative form

Lorenzo Brasco; Guido De Philippis; Bozhidar Velichkov

doi:10.1215/00127094-3120167

Faber-Krahn inequalities in sharp quantitative form

Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 W ₀ ^1,2 (ω) {right arrow, hooked} L^q(ω).

Original language	English (US)
Pages (from-to)	1777-1831
Number of pages	55
Journal	Duke Mathematical Journal
Volume	164
Issue number	9
DOIs	https://doi.org/10.1215/00127094-3120167
State	Published - 2015

ASJC Scopus subject areas

General Mathematics

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abstract = "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 Poincar{\'e}-Sobolev constant for the embeddings W 0 1,2 (ω) {right arrow, hooked} Lq(ω).",

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Faber-Krahn inequalities in sharp quantitative form

Abstract

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