Higher order pointwise differential for distribution
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915182765146112 |
|---|---|
| author | Liu, Yu-Tong |
| author_facet | Liu, Yu-Tong |
| contents | The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to a negative order Sobolev functions. Our main results prove Borel regularity, Lusin approximation, rectifiability, and a Rademacher theorem for these pointwise differentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order pointwise differential for distribution Liu, Yu-Tong Classical Analysis and ODEs 46F10 (Primary), 26B05, 41A58 (Secondary) The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to a negative order Sobolev functions. Our main results prove Borel regularity, Lusin approximation, rectifiability, and a Rademacher theorem for these pointwise differentials. |
| title | Higher order pointwise differential for distribution |
| topic | Classical Analysis and ODEs 46F10 (Primary), 26B05, 41A58 (Secondary) |
| url | https://arxiv.org/abs/2412.17691 |