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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2012
- DOI:
- 10.48550/arXiv.1207.0859
- arXiv:
- arXiv:1207.0859
- Bibcode:
- 2012arXiv1207.0859A
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- Mathematics - Functional Analysis;
- 35R15 (Primary) 35J25;
- 42B25;
- 46E35;
- 47D05;
- 60H07 (Secondary)
- E-Print:
- 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 The main change is a correction in Theorem 5.5: the second assertion has been withdrawn due to a gap in the original proof