PDE Seminar Abstracts

The asymptotic behaviour of the eigenvalues of a Robin problem

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


We consider the eigenvalues of the Laplacian with Robin-type boundary conditions u 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 λ1 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 λn has the same asymptotic behaviour, λn ~-α2, assuming only that Ω is of class C1. This is joint work with Daniel Daners.