Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911083802918912 |
|---|---|
| author | Dong, Hongjie Jeon, Seongmin |
| author_facet | Dong, Hongjie Jeon, Seongmin |
| contents | In this paper, we study solutions $u$ of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder $Q_1^+\subset \mathbb{R}^{n+1}$, where the coefficients are weighted by $x_n^α$, $α\in(-\infty,1)$. We establish higher-order boundary Schauder type estimates of $x_n^αu$ under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem Dong, Hongjie Jeon, Seongmin Analysis of PDEs 35B45, 35B65, 35K65, 35K67 In this paper, we study solutions $u$ of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder $Q_1^+\subset \mathbb{R}^{n+1}$, where the coefficients are weighted by $x_n^α$, $α\in(-\infty,1)$. We establish higher-order boundary Schauder type estimates of $x_n^αu$ under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients. |
| title | Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem |
| topic | Analysis of PDEs 35B45, 35B65, 35K65, 35K67 |
| url | https://arxiv.org/abs/2507.22663 |