A duality approach to gradient Hölder estimates for linear divergence form elliptic equations
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908773989220352 |
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| author | Saari, Olli Sun, Yuanlin Wang, Hua-Yang Wei, Yuanhong |
| author_facet | Saari, Olli Sun, Yuanlin Wang, Hua-Yang Wei, Yuanhong |
| contents | We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sparse domination bounds can be used to deduce gradient reverse Hölder inequalities for equations with non-constant coefficients from the theory for constant coefficient equations. We deal with coefficient matrices whose entries are either Hölder continuous or just uniformly continuous, leading to different results. The purpose of the approach is to highlight the connection between Schauder theory and duality of local Hardy spaces and local Hölder spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A duality approach to gradient Hölder estimates for linear divergence form elliptic equations Saari, Olli Sun, Yuanlin Wang, Hua-Yang Wei, Yuanhong Analysis of PDEs 42B37 We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sparse domination bounds can be used to deduce gradient reverse Hölder inequalities for equations with non-constant coefficients from the theory for constant coefficient equations. We deal with coefficient matrices whose entries are either Hölder continuous or just uniformly continuous, leading to different results. The purpose of the approach is to highlight the connection between Schauder theory and duality of local Hardy spaces and local Hölder spaces. |
| title | A duality approach to gradient Hölder estimates for linear divergence form elliptic equations |
| topic | Analysis of PDEs 42B37 |
| url | https://arxiv.org/abs/2512.06979 |