Estimates on eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them

Algebra/Geometry/Topology Seminar

by Andrew Hassell

Institution: ANU
Date: Tue 12th October 2010
Time: 3:15 PM
Location: Old Arts Theatre B, The University of Melbourne

Abstract: In this talk I will talk about estimating the size, at the boundary, of eigenfunctions of the Laplacian on a bounded domain in R^n. I will present estimates that are motivated by the analysis of the accuracy of a numerical method, the Method of Particular Solutions'', and show how the right sort of estimates can be used to determine precisely the accuracy of this method, in the limit as the eigenvalue tends to infinity.