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

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.


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 CÓrstea or Daniel Daners.