Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity

Article type: Research Article

Authors: Chipot, Michel^; | Roy, Prosenjit | Shafrir, Itai

Affiliations: Institut für Mathematik, Universität Zurich, Zürich, Switzerland. E-mails: {m.m.chipot, prosenjit.roy}@math.uzh.ch | Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel. E-mail: [email protected]

Note: [] Corresponding author: Michel Chipot, Institut für Mathematik, Universität Zurich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland. E-mail: [email protected]

Abstract: We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem and show in particular, that in general the limiting behavior is very different from the one for the Dirichlet boundary conditions.

Keywords: eigenvalue problem, ℓ goes to plus infinity, dimension reduction

DOI: 10.3233/ASY-131182

Journal: Asymptotic Analysis, vol. 85, no. 3-4, pp. 199-227, 2013