Nonautonomous maximal Lp-regularity under fractional Sobolev regularity in time

Fackler, Stephan

doi:10.2140/apde.2018.11.1143

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Nonautonomous maximal $L^p$-regularity under fractional Sobolev regularity in time

Stephan Fackler

Vol. 11 (2018), No. 5, 1143–1169

DOI: 10.2140/apde.2018.11.1143

Abstract

We prove nonautonomous maximal $L^{p}$ -regularity results on UMD spaces, replacing the common Hölder assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In particular, on $L^{q} (Ω)$ we obtain maximal $L^{p}$ -regularity for $p \geq 2$ and elliptic operators in divergence form with uniform VMO-modulus in space and $W^{α, p}$ -regularity for $α > \frac{1}{2}$ in time.

Keywords

nonautonomous maximal regularity, parabolic equations in divergence form, quasilinear parabolic problems

Mathematical Subject Classification 2010

Primary: 35B65

Secondary: 35K10, 35B45, 47D06

Milestones

Received: 9 January 2017

Revised: 19 June 2017

Accepted: 29 November 2017

Published: 11 April 2018

Authors

Stephan Fackler
Institute of Applied Analysis Ulm University Ulm Germany

Vol. 11, No. 5, 2018