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

# 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.

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