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

Matthias Geissert; Luca Lorenzi; Roland Schnaubelt

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

Analysis of PDEs 2009-03-19 v1 Classical Analysis and ODEs

Authors: Matthias Geissert , Luca Lorenzi , Roland Schnaubelt

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.

Keywords

operator theory and elliptic operators maximal operators regularity for elliptic equations

Cite

@article{arxiv.0903.3117,
  title  = {$L^p$--regularity for parabolic operators with unbounded time--dependent coefficients},
  author = {Matthias Geissert and Luca Lorenzi and Roland Schnaubelt},
  journal= {arXiv preprint arXiv:0903.3117},
  year   = {2009}
}