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Capacité et inégalité de Faber-Krahn dans Rn
Auteur(s)
Bertrand, Jérôme
Date de parution
2006-4-18
In
Journal of Functional Analysis
Vol.
1
No
232
De la page
1
A la page
28
Résumé
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 generalises 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.
Identifiants
Type de publication
journal article
