The asymptotic behaviour of the eigenvalues of a Robin problem

James Kennedy
University of Sydney
10 May 2010, 3-4pm, Carslaw Room 273

Abstract

We consider the eigenvalues of the Laplacian with Robin-type boundary conditions {∂u\over ∂ν} = αu. Here we assume α > 0, in contrast to the usual case where α < 0. In recent years, increasing attention has been devoted to the behaviour of the smallest eigenvalue {λ}_{1} as the parameter α →∞ under various assumptions on the underlying domain. After surveying existing results in this area, we will prove using a test function argument that every eigenvalue {λ}_{n} has the same asymptotic behaviour, {λ}_{n} ~-{α}^{2}, assuming only that Ω is of class {C}^{1}. This is joint work with Daniel Daners.

Check also the PDE Seminar page. Enquiries to Florica Cîrstea or Daniel Daners.