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arXiv:1809.08580 [math.AP]AbstractReferencesReviewsResources

Hadamard Asymptotics for Eigenvalues of the Dirichlet Laplacian

Vladimir Kozlov, Johan Thim

Published 2018-09-23Version 1

This paper is dedicated to the classical Hadamard formula for asymptotics of eigenvalues of the Dirichlet-Laplacian under perturbations of the boundary. We prove that the Hadamard formula still holds for $C^1$-domains with $C^1$-perturbations. We also derive an optimal estimate for the remainder term in the $C^{1,\alpha}$-case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.

Categories: math.AP, math.SP
Subjects: 35P05, 47A75, 49R05, 47A55
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