On regularity of weak solutions to linear parabolic systems with measurable coefficients

Abstract

We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solutions are locally H{ö}lder continuous Lp valued functions for some p > 2.

23 pages. Proof of Lemma 3.3 corrected. Final version to appear in J. Math. Pures Appl