Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 9 (2015), 1777-1831.
Faber–Krahn inequalities in sharp quantitative form
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 .
Duke Math. J., Volume 164, Number 9 (2015), 1777-1831.
Received: 14 June 2013
Revised: 21 September 2014
First available in Project Euclid: 15 June 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47A75: Eigenvalue problems [See also 47J10, 49R05]
Secondary: 49Q20: Variational problems in a geometric measure-theoretic setting 49R05: Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)
Brasco, Lorenzo; De Philippis, Guido; Velichkov, Bozhidar. Faber–Krahn inequalities in sharp quantitative form. Duke Math. J. 164 (2015), no. 9, 1777--1831. doi:10.1215/00127094-3120167. https://projecteuclid.org/euclid.dmj/1434377461