Vol. 11, No. 5, 2018

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

Stephan Fackler

Vol. 11 (2018), No. 5, 1143–1169
Abstract

We prove nonautonomous maximal Lp-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 Lq(Ω) we obtain maximal Lp-regularity for p 2 and elliptic operators in divergence form with uniform VMO-modulus in space and Wα,p-regularity for α > 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