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

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  • 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 Hölder regularity is given for the solutions and their derivatives up to order $2b-1.$
    Mathematics Subject Classification: 35K40 (primary); 35R05, 35B45, 35B65, 42B20,46E35 (secondary).


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