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

TL;DR

This paper proves maximal regularity results for nonautonomous Ornstein-Uhlenbeck operators with unbounded, time-dependent coefficients in $L^p$-spaces, extending understanding of parabolic operators with variable coefficients.

Contribution

It establishes the maximal $L^p$-regularity for a class of elliptic and parabolic operators with unbounded, time-dependent coefficients, a novel extension in the theory.

Findings

Maximal regularity for nonautonomous Ornstein-Uhlenbeck operators in $L^p$-spaces.

Extension of maximal regularity results to operators with unbounded, time-dependent coefficients.

Results hold for $p$ in (1, +∞).

Abstract

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.