L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains

Abstract

We present some new results on analytic Ornstein-Uhlenbeck semigroups and use them to extend recent work of Da Prato and Lunardi for Ornstein-Uhlenbeck semigroups on open domains O to the non-symmetric case. Denoting the generator of the semigroup by L_O, we obtain sufficient conditions in order that the domain Dom(\sqrt{-L_O}) be a first order Sobolev space.

23 pages, revised version, to appear in J. Evol. Eq. The main change is a correction in Theorem 5.5: the second assertion has been withdrawn due to a gap in the original proof