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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.13017 |
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| _version_ | 1866911262511726592 |
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| author | Azzam, Jonas Mourgoglou, Mihalis Villa, Michele |
| author_facet | Azzam, Jonas Mourgoglou, Mihalis Villa, Michele |
| contents | We prove $L^p$ quantitative differentiability estimates for functions defined on uniformly rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-type theorem holds in this context: the $L^p$ norm of the gradient of a Sobolev function $f: E \to \mathbb{R}$ is comparable to the $L^p$ norm of a new square function measuring both the affine deviation of $f$ and how flat the subset $E$ is. A corollary dealing with extensions and traces of Sobolev functions may be found in a companion article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative differentiability on uniformly rectifiable sets Azzam, Jonas Mourgoglou, Mihalis Villa, Michele Classical Analysis and ODEs Analysis of PDEs 46E35 We prove $L^p$ quantitative differentiability estimates for functions defined on uniformly rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-type theorem holds in this context: the $L^p$ norm of the gradient of a Sobolev function $f: E \to \mathbb{R}$ is comparable to the $L^p$ norm of a new square function measuring both the affine deviation of $f$ and how flat the subset $E$ is. A corollary dealing with extensions and traces of Sobolev functions may be found in a companion article. |
| title | Quantitative differentiability on uniformly rectifiable sets |
| topic | Classical Analysis and ODEs Analysis of PDEs 46E35 |
| url | https://arxiv.org/abs/2306.13017 |