Regularizing properties for transition semigroups and semilinear parabolic
equations in Banach spaces
Federica Masiero, Universita di Milano-Bicocca
Abstract
We study regularizing properties for transition semigroups related to Ornstein
Uhlenbeck processes with values in a Banach space E which is continuously
and densely embedded in a real and separable Hilbert space $H$. Namely we
study conditions under which the transition semigroup maps continuous and
bounded functions into differentiable functions. Via a Girsanov type theorem
such properties extend to perturbed Ornstein Uhlenbeck processes. We apply the
results to solve in mild sense semilinear versions of Kolmogorov equations in
E.
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