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 C1,α-case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.
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