A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908740100292608 |
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| author | Choi, Jae-Hwan Ryu, Junhee |
| author_facet | Choi, Jae-Hwan Ryu, Junhee |
| contents | We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and to the critical case of integer-order regularity. In addition, nonzero initial data are treated in the optimal trace space via a sharp trace theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces Choi, Jae-Hwan Ryu, Junhee Analysis of PDEs 35K15, 35B65, 26A16, 35D35 We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and to the critical case of integer-order regularity. In addition, nonzero initial data are treated in the optimal trace space via a sharp trace theorem. |
| title | A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces |
| topic | Analysis of PDEs 35K15, 35B65, 26A16, 35D35 |
| url | https://arxiv.org/abs/2512.24020 |