Capacite et inegalite de Faber-Krahn dans l'espace euclidien
Differential Geometry
2007-05-23 v1 Spectral Theory
Abstract
In this paper, we define a new capacity which allows us to control the behaviour of the Dirichlet spectrum of a compact Riemannian manifold with boundary, with "small" subsets (which may intersect the boundary) removed. This result generalizes a classical result of Rauch and Taylor ("the crushed ice theorem"). In the second part, we show that the Dirichlet spectrum of a sequence of bounded Euclidean domains converges to the spectrum of a ball with the same volume, if the first eigenvalue of these domains converges to the first eigenvalue of a ball.
Cite
@article{arxiv.math/0504170,
title = {Capacite et inegalite de Faber-Krahn dans l'espace euclidien},
author = {Jerome Bertrand and Bruno Colbois},
journal= {arXiv preprint arXiv:math/0504170},
year = {2007}
}