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
... [Show full abstract] Hadamard formula is not valid.