Schauder type estimates for degenerate or singular parabolic systems with partially DMO coefficients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911174863355904 |
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| author | Dong, Hongjie Jeon, Seongmin |
| author_facet | Dong, Hongjie Jeon, Seongmin |
| contents | We study elliptic and parabolic systems in divergence form with degenerate or singular coefficients. Under the conormal boundary condition on the flat boundary, we establish boundary Schauder type estimates when the coefficients have partially Dini mean oscillation. Moreover, as an application, we achieve $k^{\text{th}}$ higher-order boundary Harnack principles for uniformly parabolic equations with Hölder coefficients, extending a recent result in [Audrito-Fioravanti-Vita 25] from $k\ge2$ to any $k\ge1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schauder type estimates for degenerate or singular parabolic systems with partially DMO coefficients Dong, Hongjie Jeon, Seongmin Analysis of PDEs 35B45, 35B65, 35K65, 35K67 We study elliptic and parabolic systems in divergence form with degenerate or singular coefficients. Under the conormal boundary condition on the flat boundary, we establish boundary Schauder type estimates when the coefficients have partially Dini mean oscillation. Moreover, as an application, we achieve $k^{\text{th}}$ higher-order boundary Harnack principles for uniformly parabolic equations with Hölder coefficients, extending a recent result in [Audrito-Fioravanti-Vita 25] from $k\ge2$ to any $k\ge1$. |
| title | Schauder type estimates for degenerate or singular parabolic systems with partially DMO coefficients |
| topic | Analysis of PDEs 35B45, 35B65, 35K65, 35K67 |
| url | https://arxiv.org/abs/2502.08926 |