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

2004/10/19 by Palagachev, Dian K., Softova, Lubomira G.
#35B45 35B65 #35K40 (primary) 35R05 #42B20 #46E35 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0410415

Abstract

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.

Related

• Generalized Morrey regularity for parabolic equations with discontinuity data
• Partial regularity for parabolic systems with VMO-coefficients
• Estimates in the Generalized Morrey Spaces for Linear Parabolic Systems
• L^p-parabolic regularity and non-degenerate Ornstein-Uhlenbeck type operators
• Fine regularity for elliptic systems with discontinuous ingredients