On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909913431670784 |
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| author | Shlapunov, Alexander Vilkov, Pavel |
| author_facet | Shlapunov, Alexander Vilkov, Pavel |
| contents | We investigate the problem on Runge pairs for Sobolev solutions of strongly uniformly parabolic systems in non-cylindrical domains of a special kind. We prove that if the coefficients of a parabolic operator are constant, then two domains with sufficiently smooth boundaries, no parts of which are parallel to the plane $t=0$, form a Runge pair if and only if the complements of any section of the larger domain to the section of the smaller domain by planes $t = const$, have no compact components in the larger section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces Shlapunov, Alexander Vilkov, Pavel Analysis of PDEs Primary 35A35, Secondary 35N17, 35K25 We investigate the problem on Runge pairs for Sobolev solutions of strongly uniformly parabolic systems in non-cylindrical domains of a special kind. We prove that if the coefficients of a parabolic operator are constant, then two domains with sufficiently smooth boundaries, no parts of which are parallel to the plane $t=0$, form a Runge pair if and only if the complements of any section of the larger domain to the section of the smaller domain by planes $t = const$, have no compact components in the larger section. |
| title | On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces |
| topic | Analysis of PDEs Primary 35A35, Secondary 35N17, 35K25 |
| url | https://arxiv.org/abs/2511.15216 |