Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary
نویسندگان
چکیده
In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic in the spatial and boundaryvariation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphic operator-valued functions. 2000 Mathematics Subject Classification: 35J05, 35C15, 44P05
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