Matrix parabolic problems in Sobolev spaces of generalized smoothness
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914531690676224 |
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| author | Los, Valerii Mikhailets, Vladimir Murach, Aleksandr |
| author_facet | Los, Valerii Mikhailets, Vladimir Murach, Aleksandr |
| contents | We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functions are used to characterize supplementary generalized smoothness that cannot be determined by number indexes. We prove that this problem induces topological isomorphisms on appropriate pairs of such spaces. As an application, we give sufficient and necessary conditions for the problem solutions to have prescribed generalized regularity expressed in terms of these spaces. Their use allows obtaining exact conditions for indicated generalized partial derivatives of the solutions to be continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03967 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix parabolic problems in Sobolev spaces of generalized smoothness Los, Valerii Mikhailets, Vladimir Murach, Aleksandr Analysis of PDEs 35K35, 46E35 We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functions are used to characterize supplementary generalized smoothness that cannot be determined by number indexes. We prove that this problem induces topological isomorphisms on appropriate pairs of such spaces. As an application, we give sufficient and necessary conditions for the problem solutions to have prescribed generalized regularity expressed in terms of these spaces. Their use allows obtaining exact conditions for indicated generalized partial derivatives of the solutions to be continuous. |
| title | Matrix parabolic problems in Sobolev spaces of generalized smoothness |
| topic | Analysis of PDEs 35K35, 46E35 |
| url | https://arxiv.org/abs/2605.03967 |