Anisotropic gradient rearrangement of BV functions and applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910223675949056 |
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| author | Paoli, Gloria Yang, Yabo |
| author_facet | Paoli, Gloria Yang, Yabo |
| contents | In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in [Amato-Gentile-Nitsch-Trombetti, 2024] by separating the absolutely continuous part of the anisotropic gradient from its singular part. Our main result is an $L^1$ comparison between the function and its anisotropic symmetrization. Moreover, as an application, we
derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anisotropic gradient rearrangement of BV functions and applications Paoli, Gloria Yang, Yabo Analysis of PDEs 26A45, 35A23, 35B45, 35J60 In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in [Amato-Gentile-Nitsch-Trombetti, 2024] by separating the absolutely continuous part of the anisotropic gradient from its singular part. Our main result is an $L^1$ comparison between the function and its anisotropic symmetrization. Moreover, as an application, we derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity. |
| title | Anisotropic gradient rearrangement of BV functions and applications |
| topic | Analysis of PDEs 26A45, 35A23, 35B45, 35J60 |
| url | https://arxiv.org/abs/2605.15849 |