**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 Cîrstea or Daniel Daners.