Hadamard Asymptotics for Eigenvalues of the Dirichlet Laplacian

2018/09/23 by Kozlov, Vladimir, Thim, Johan
#35P05 #47A55 #47A75 #49R05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1809.08580

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 C¹-domains with C¹-perturbations. We also derive an optimal estimate for the remainder term in the C^1,α-case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.

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