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.
A priori estimates and precise regularity for parabolic systems with discontinuous data / Palagachev, D; Softova, L. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 13:3(2005), pp. 721-742. [10.3934/dcds.2005.13.721]
A priori estimates and precise regularity for parabolic systems with discontinuous data
Palagachev, D;
2005-01-01
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 Holder regularity is given for the solutions and their derivatives up to order 2b - 1.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
