$L^p$--regularity for parabolic operators with unbounded time--dependent coefficients

Geissert, Matthias; Lorenzi, Luca; Schnaubelt, Roland

$L^p$--regularity for parabolic operators with unbounded time--dependent coefficients

Authors

Geissert, Matthias

Lorenzi, Luca

Schnaubelt, Roland

Description

We establish the maximal regularity for nonautonomous Ornstein-Uhlenbeck operators in $L^p$-spaces with respect to a family of invariant measures, where $p\in (1,+\infty)$. This result follows from the maximal $L^p$-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on $L^p(\R^N)$ with Lebesgue measure.