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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.01168 |
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| _version_ | 1866911296164724736 |
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| author | Krylov, N. V. |
| author_facet | Krylov, N. V. |
| contents | We prove an existence and uniqueness theorem for second-order parabolic equations in the whole space with constant zeroth-order coefficient in mixed-norm Morrey-Sobolev spaces. The main coefficient $a$ is assumed to be measurable in $t$ and BMO in $x$ and the first-order coefficients $b$ are in an appropriate mixed-norm Morrey classes (thus admitting rather rough singularities). The mixed-norm Morrey-Sobolev spaces are ``odd'' in the sense that the interior integration in the formula defining the norm is performed with respect to $t$ and not to $x$ as is customary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On solvability of parabolic equations with singular coefficients in odd mixed-norm Morrey-Sobolev spaces Krylov, N. V. Analysis of PDEs 35K10, 35K67 We prove an existence and uniqueness theorem for second-order parabolic equations in the whole space with constant zeroth-order coefficient in mixed-norm Morrey-Sobolev spaces. The main coefficient $a$ is assumed to be measurable in $t$ and BMO in $x$ and the first-order coefficients $b$ are in an appropriate mixed-norm Morrey classes (thus admitting rather rough singularities). The mixed-norm Morrey-Sobolev spaces are ``odd'' in the sense that the interior integration in the formula defining the norm is performed with respect to $t$ and not to $x$ as is customary. |
| title | On solvability of parabolic equations with singular coefficients in odd mixed-norm Morrey-Sobolev spaces |
| topic | Analysis of PDEs 35K10, 35K67 |
| url | https://arxiv.org/abs/2512.01168 |