Capacite et inegalite de Faber-Krahn dans l'espace euclidien

Details Capacite et inegalite de Faber-Krahn dans l'espace euclidien Capacite et inegalite de Faber-Krahn dans l'espace euclidien

2005-04-08

arxiv.org/abs/math/0504170v1

Mathematics

Differential Geometry

Scientific paper

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.

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