**SMS scnews item created by Daniel Daners at Wed 10 Aug 2011 0900**

Type: Seminar

Distribution: World

Expiry: 18 Aug 2011

**Calendar1: 18 Aug 2011 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@bari.maths.usyd.edu.au

### PDE Seminar

# The Dirichlet-to-Neumann operator on rough domains

### ter Elst

Tom ter Elst

University of Auckland, NZ

Thu 18 August 2010 2-3pm, Carslaw 829 (Access Grid Room), note the unusual day.

## Abstract

We consider a bounded connected open set \(\Omega \subset \mathbb R^d\) whose
boundary $\Gamma$ has a finite \((d-1)\)-dimensional Hausdorff measure.
Then we define the Dirichlet-to-Neumann operator \(D_0\) on
\(L_2(\Gamma)\) by form methods. The operator \(-D_0\) is self-adjoint
and generates a contractive \(C_0\)-semigroup \(S = (S_t)_{t > 0}\) on
\(L_2(\Gamma)\). We show that the asymptotic behaviour of \(S_t\) as \(t
\to \infty\) is related to properties of the trace of functions in
\(H^1(\Omega)\) which \(\Omega\) may or may not have.

The talk is based on joint work with W. Arendt (Ulm).

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