Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces
نویسنده
چکیده
In the present paper we consider the transition semigroup Pt related to some stochastic reaction-diusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing eect in the Banach space of continuous functions C O, where O R is a bounded open set. In L2 O the only result proved is the strong Feller property, for d 1. Here we are able to prove that if f 2 C1 R and d 3, then Ptu 2 C1 b C O for any u 2 Bb C O 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 stochastic control. Mathematics Subject Classi®cation (1991): 60J35, 60H15, 35K20, 60J25.
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