Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

Details Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

2006-12-26

arxiv.org/abs/math/0612764v1

Mathematics

Analysis of PDEs

Scientific paper

10.1134/S0965542506010118

We study the asymptotic behavior of the solutions of a spectral problem for
the Laplacian in a domain with rapidly oscillating boundary. We consider the
case where the eigenvalue of the limit problem is multiple. We construct the
leading terms of the asymptotic expansions for the eigenelements and verify the
asymptotics.

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