We consider a bounded connected open set whose boundary has a finite -dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator on by form methods. The operator is self-adjoint and generates a contractive -semigroup on . We show that the asymptotic behaviour of as is related to properties of the trace of functions in which may or may not have.
The talk is based on joint work with W. Arendt (Ulm).