SMS scnews item created by Daniel Daners at Fri 26 Aug 2011 1730
Type: Seminar
Distribution: World
Expiry: 29 Aug 2011
Calendar1: 29 Aug 2011 1400-1500
CalLoc1: Eastern Ave 405
Auth: daners@bari.maths.usyd.edu.au

PDE Seminar

The Dirichlet problem by variational methods

Daners

Daniel Daners
University of Sydney
Mon 29 August 2011 2-3pm, Eastern Avenue Seminar Room 405

Abstract

We consider the classical Dirichlet problem for harmonic functions on an open bounded set in \(\mathbb R^N\) with continuous boundary data. Dirichlet's principle provides a variational method to solve the problem. As an example by Hadamard shows, the Dirichlet principle is not applicable for all boundary data, but only for those which have an extension to a function \(\Phi\in H^1(\Omega)\).

The aim of the talk is to show that there is a variational method to solve the Dirichlet problem even if there is no extension of the boundary data to \(H^1(\Omega)\). We present an approach which works if there is an extension \(\Phi\) such that \(\Delta\Phi\in H^{-1}(\Omega)\), which is a considerably weaker assumption than the one required for Dirichlet's principle. This is joint work with W Arendt.

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


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