Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains

Boundary Value Problems20102010:853717

DOI: 10.1155/2010/853717

Received: 31 July 2010

Accepted: 11 November 2010

Published: 30 November 2010

Abstract

By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural local problem is not an eigenvalue problem.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Chalmers University of Technology

Copyright

© Hermann Douanla. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.