Hadamard Asymptotics for Eigenvalues of the Dirichlet Laplacian
Analysis of PDEs
2018-09-25 v1 Spectral Theory
Abstract
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 -domains with -perturbations. We also derive an optimal estimate for the remainder term in the -case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.
Keywords
Cite
@article{arxiv.1809.08580,
title = {Hadamard Asymptotics for Eigenvalues of the Dirichlet Laplacian},
author = {Vladimir Kozlov and Johan Thim},
journal= {arXiv preprint arXiv:1809.08580},
year = {2018}
}