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 ut − divA(Du) = 0, (x,t) ∈ Ω ×(−T,0) = ΩT , where Ω ⊂ Rn is a bounded domain, T >0, A : RnN → RN and u : ΩT → RN. 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. © 2007 Elsevier Inc. All rights reserved.