Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary |
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Authors: | M I Cherdantsev |
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Institution: | (1) Ufa State Aviation Technical University, Ufa, Russia |
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Abstract: | In this paper, we consider eigenvalue problems for the Laplace operator in three-dimensional domains with singularly perturbed boundary. Perturbations are generated by a complementary Dirichlet boundary condition on a small nonclosed surface inside the domain. The convergence and the asymptotic behavior of simple eigenvalues of the problem are considered.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 299–307.Original Russian Text Copyright © 2005 by M. I. Cherdantsev. |
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Keywords: | Dirichlet boundary-value problem Laplace operator singular perturbation asymptotics of eigenvalues Sobolev spaces |
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