This is the abstract of the paper
  "Wiener Regularity and Heat Semigroups on Spaces of Continuous Functions"=
       =20
by Wolfgang Arendt and Philippe B=E9nilan.

For the whole paper send the command

  get evolve-l 99-00012

to: "listserv@rz.uni-karlsruhe.de".

Instead you may get the paper at
  "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html"
too.

Abstract: Let $\Omega \subset \R^N$ be open. It is shown that the Dirichlet
Laplacian generates a (holomorphic) $C_0$-semigroup on $C_0(\Omega)$
if and only if $\Omega$ is regular in the sense of Wiener. The same
result remains true for elliptic operators in divergence form.