Let Ω be an exterior domain in It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.
