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 typeut−divA(Du)=0,(x,t)∈Ω×(−T,0)=ΩT, where Ω⊂RnΩ⊂Rn is a bounded domain, T>0T>0, A:RnN→RNA:RnN→RN and u:ΩT→RNu: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.