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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/2303.00834 |
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| _version_ | 1866914859719852032 |
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| author | Comi, Giovanni E. Stefani, Giorgio |
| author_facet | Comi, Giovanni E. Stefani, Giorgio |
| contents | Given $α\in(0,1]$ and $p\in[1,+\infty]$, we define the space $\mathscr{DM}^{α,p}(\mathbb R^n)$ of $L^p$ vector fields whose $α$-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the $α$-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula Comi, Giovanni E. Stefani, Giorgio Functional Analysis Primary 26A33. Secondary 26B20, 26B30 Given $α\in(0,1]$ and $p\in[1,+\infty]$, we define the space $\mathscr{DM}^{α,p}(\mathbb R^n)$ of $L^p$ vector fields whose $α$-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the $α$-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples. |
| title | Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula |
| topic | Functional Analysis Primary 26A33. Secondary 26B20, 26B30 |
| url | https://arxiv.org/abs/2303.00834 |