Sobolev sheaves on the plane
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912725292023808 |
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| author | Oudrane, M'hammed |
| author_facet | Oudrane, M'hammed |
| contents | In this paper, we show that for any integer $k \in \mathbb{N}$ there exists a Sobolev sheaf (in the sense of Lebeau) on any definable site of $\mathbb{R}^2$ that agrees with Sobolev spaces on cuspidal domains. We also provide a complete computation of the cohomology of these sheaves using the notion of 'Good direction' introduced by Valette. This paper serves as an introduction to a more general project on the sheafification of Sobolev spaces in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sobolev sheaves on the plane Oudrane, M'hammed Metric Geometry In this paper, we show that for any integer $k \in \mathbb{N}$ there exists a Sobolev sheaf (in the sense of Lebeau) on any definable site of $\mathbb{R}^2$ that agrees with Sobolev spaces on cuspidal domains. We also provide a complete computation of the cohomology of these sheaves using the notion of 'Good direction' introduced by Valette. This paper serves as an introduction to a more general project on the sheafification of Sobolev spaces in higher dimensions. |
| title | Sobolev sheaves on the plane |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2308.08077 |