A priori estimates and precise regularity for parabolic systems with discontinuous data

We deal with linear parabolic (in the sense of Petrovskii) systems of order 2b with discontinuous principal coefficients. A priori estimates in Sobolev and Sobolev-Morrey spaces are proved for the strong solutions by means of potential analysis and boundedness of certain singular integral operators with kernels of mixed homogeneity. As a byproduct, precise characterization of the Morrey, BMO and Holder regularity is given for the solutions and their derivatives up to order 2b - 1.