L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains
Probability
2012-10-29 v2 Analysis of PDEs
Functional Analysis
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.
Cite
@article{arxiv.1207.0859,
title = {L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains},
author = {Joyce Assaad and Jan van Neerven},
journal= {arXiv preprint arXiv:1207.0859},
year = {2012}
}
Comments
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 The main change is a correction in Theorem 5.5: the second assertion has been withdrawn due to a gap in the original proof