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April  2005, 13(3): 721-742. doi: 10.3934/dcds.2005.13.721

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

Dian Palagachev 1, and  Lubomira Softova 2,

1. 

Department of Mathematics, Polytechnic University of Bari, 4 E. Orabona Str., 70 125 Bari, Italy
2. 

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Received  September 2004 Revised  March 2005 Published  May 2005

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 $2b-1.$
Keywords: Hölder regularity., Morrey spaces, Parabolic systems, a priori estimates.
Mathematics Subject Classification: 35K40 (primary); 35R05, 35B45, 35B65, 42B20,46E35 (secondary.
Citation: Dian Palagachev, Lubomira Softova. A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 721-742. doi: 10.3934/dcds.2005.13.721
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