A'priori estimates and precise regularity for parabolic systems with discontinuous data
Analysis of PDEs
2025-12-10 v2
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 H\"older 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.
Keywords
Cite
@article{arxiv.math/0410415,
title = {A'priori estimates and precise regularity for parabolic systems with discontinuous data},
author = {Dian K. Palagachev and Lubomira G. Softova},
journal= {arXiv preprint arXiv:math/0410415},
year = {2025}
}
Comments
15 pages, 1 figure