Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1258

 Title: Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary Authors: Khelifi, Abdessatar Keywords: EigenvaluesEigenfunctionsLaplace OperatorDomain PerturbationIntegral EquationAnalyticity35J0535C1544P05 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 URI: http://hdl.handle.net/10525/1258 ISSN: 1311-0454 Appears in Collections: 2005

Files in This Item:

File Description SizeFormat