This article is cited in 4 papers

Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary

M. I. Cherdantsev

Ufa State Aviation Technical University

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.

UDC: 571.958

Received: 24.08.2004
Revised: 27.12.2004

DOI: 10.4213/mzm2575

 English version: Mathematical Notes, 2005, 78:2, 270–278

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