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Title: Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary
Authors: Khelifi, Abdessatar
Keywords: Eigenvalues
Laplace Operator
Domain Perturbation
Integral Equation
Issue Date: 2005
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 8, No 3, (2005), 277p-298p
Abstract: 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 boundary-variation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphic operator-valued functions.
Description: 2000 Mathematics Subject Classification: 35J05, 35C15, 44P05
ISSN: 1311-0454
Appears in Collections:2005

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