In this paper, we consider the dependence of the Dirichlet eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain of definition. We prove that the dependence of a certain eigenvalue and of the corresponding eigenspace is analytic on the set of perturbations that leave the multiplicity constant.
An analyticity result for the dependence of multiple eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain
LAMBERTI, PIER DOMENICO;LANZA DE CRISTOFORIS, MASSIMO
2002
Abstract
In this paper, we consider the dependence of the Dirichlet eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain of definition. We prove that the dependence of a certain eigenvalue and of the corresponding eigenspace is analytic on the set of perturbations that leave the multiplicity constant.
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