  We consider a bounded connected open set $\Omega \subset {\rm R}^d$ 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.
