**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**

Auth: daners@p7153.pc.maths.usyd.edu.au

### PDE Seminar

# The asymptotic behaviour of the eigenvalues of a Robin problem

### Kennedy

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.