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

Fuente: arXiv
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Main Authors: Palagachev, Dian K., Softova, Lubomira G.
Format: Preprint
Published: 2004
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author Palagachev, Dian K.
Softova, Lubomira G.
author_facet Palagachev, Dian K.
Softova, Lubomira G.
contents We deal with linear parabolic (in 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. Some counterexamples of recent publications announcing estimates similar to the obtained here are also given.
format Preprint
id arxiv_https___arxiv_org_abs_math_0410415
institution arXiv
publishDate 2004
record_format arxiv
spellingShingle A'priori estimates and precise regularity for parabolic systems with discontinuous data
Palagachev, Dian K.
Softova, Lubomira G.
Analysis of PDEs
35K40 (primary) 35R05, 35B45 35B65, 42B20, 46E35 (secondary)
We deal with linear parabolic (in 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. Some counterexamples of recent publications announcing estimates similar to the obtained here are also given.
title A'priori estimates and precise regularity for parabolic systems with discontinuous data
topic Analysis of PDEs
35K40 (primary) 35R05, 35B45 35B65, 42B20, 46E35 (secondary)
url https://arxiv.org/abs/math/0410415