SMS scnews item created by Daniel Daners at Tue 4 May 2010 1544
Type: Seminar
Distribution: World
Expiry: 10 May 2010
Calendar1: 10 May 2010 1500-1600
CalLoc1: Carslaw 273

PDE Seminar

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\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 CÓrstea or Daniel Daners.

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