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.
|Titolo:||A priori estimates and precise regularity for parabolic systems with discontinuous data|
|Data di pubblicazione:||2005|
|Digital Object Identifier (DOI):||10.3934/dcds.2005.13.721|
|Appare nelle tipologie:||1.1 Articolo in rivista|