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

Dian Palagachev; Lubomira Softova

doi:10.3934/dcds.2005.13.721

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2005, Volume 13, Issue 3: 721-742. Doi: 10.3934/dcds.2005.13.721

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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
2.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia

Received: August 31, 2004

Revised: February 28, 2005

Published: March 2005

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Abstract

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 $2b-1.$

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Mathematics Subject Classification: 35K40 (primary); 35R05, 35B45, 35B65, 42B20,46E35 (secondary).

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