A'priori estimates and precise regularity for parabolic systems with discontinuous data
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| Format: | Preprint |
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2004
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| _version_ | 1866917135476850688 |
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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 |
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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 |