PDE Seminar Abstracts

The Dirichlet-to-Neumann operator on rough domains

Tom ter Elst
University of Auckland, New Zealand
Thursday 18 August 2011 2-3pm, Carslaw 829 (Access Grid Room)


We consider a bounded connected open set Ω d whose boundary Γ has a finite (d - 1)-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D0 on L2(Γ) by form methods. The operator - D0 is self-adjoint and generates a contractive C0-semigroup S = (St)t>0 on L2(Γ). We show that the asymptotic behaviour of St as t is related to properties of the trace of functions in H1(Ω) which Ω may or may not have.

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