A priori estimates and precise regularity for parabolic systems with discontinuous data
Dian Palagachev - Department of Mathematics, Polytechnic University of Bari, 4 E. Orabona Str., 70 125 Bari, Italy (email)
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 $2b-1.$
Keywords: Parabolic systems, a priori estimates, Morrey spaces, Hölder
Received: September 2004; Revised: March 2005; Available Online: May 2005.
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