Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains
Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden
Boundary Value Problems 2010, 2010:853717 doi:10.1155/2010/853717Published: 30 November 2010
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.