Faber-Krahn inequalities in sharp quantitative form

Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov

Research output: Contribution to journalArticlepeer-review


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} Lq(ω).

Original languageEnglish (US)
Pages (from-to)1777-1831
Number of pages55
JournalDuke Mathematical Journal
Issue number9
StatePublished - 2015

ASJC Scopus subject areas

  • General Mathematics


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