Abstract
In the present paper we consider the transition semigroup Pt related to some stochastic reaction-diAusion equations with the non- linear term f having polynomial growth and satisfying some dis- sipativity conditions. We are proving that it has a regularizing eAect in the Banach space of continuous functions COOU, where O R d is a bounded open set. In L 2 OOU the only result proved is the strong Feller property, for da 1. Here we are able to prove that if f 2 C 1 ORU and d 3, then Ptu2 C 1 b OCOOUU for any u2 BbOCOOUU and t > 0. An important application is to the study of the ergodic properties of the system. These results are also of interest for some problem in sto- chastic control.
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