1687-2770-2010-853717 1687-2770 Research Article <p>Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains</p> DouanlaHermanndouanla@chalmers.se

Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden

 Boundary Value Problems 1687-2770 2010 2010 1 853717 http://www.boundaryvalueproblems.com/content/2010/1/853717 10.1155/2010/853717 31720101111201030112010 2010Hermann Douanla.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.

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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