Partial regularity and singular set of solutions to second order parabolic systems

In this paper we deal with the study of regularity properties of weak solutions to nonlinear, second-order parabolic systems of the type u(t) - div A(Du) = 0, (x, t) is an element of Omega x (-T, 0) = Omega(T), where Omega subset of R-n is a bounded domain, T > 0, A : R-nN -> R-N and u : Omega(T) -> R-N. In particular we provide higher fractional differentiability, partial regularity and estimates for the dimension of the singular sets of weak solutions under minimal regularity hypotheses on A. (C) 2007 Elsevier Inc. All rights reserved.