Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case
Analysis of PDEs
2009-11-11 v1
Abstract
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.
Cite
@article{arxiv.math/0612764,
title = {Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case},
author = {Youcef Amirat and Gregory A. Chechkin and Rustem R. Gadyl'shin},
journal= {arXiv preprint arXiv:math/0612764},
year = {2009}
}