Sparse gradient bounds for divergence form elliptic equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916398397128704 |
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| author | Saari, Olli Wang, Hua-Yang Wei, Yuanhong |
| author_facet | Saari, Olli Wang, Hua-Yang Wei, Yuanhong |
| contents | We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO coefficients and a result for linear equations with Dini continuous coefficients. In addition, we provide an abstract theorem conditional on PDE estimates available. The linear results have the full range of weighted estimates with Muckenhoupt weights as a consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse gradient bounds for divergence form elliptic equations Saari, Olli Wang, Hua-Yang Wei, Yuanhong Analysis of PDEs Classical Analysis and ODEs We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO coefficients and a result for linear equations with Dini continuous coefficients. In addition, we provide an abstract theorem conditional on PDE estimates available. The linear results have the full range of weighted estimates with Muckenhoupt weights as a consequence. |
| title | Sparse gradient bounds for divergence form elliptic equations |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2402.16213 |