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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2302.11332 |
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| _version_ | 1866913331873316864 |
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| author | Amato, Vincenzo Gentile, Andrea Nitsch, Carlo Trombetti, Cristina |
| author_facet | Amato, Vincenzo Gentile, Andrea Nitsch, Carlo Trombetti, Cristina |
| contents | In this paper, we introduce a symmetrization technique for the gradient of a $\BV$ function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an $\text{\emph{L}}^{\text{1}}$ comparison between the function and its symmetrized.
Furthermore, we apply this result to obtain Saint-Venant type inequalities for some geometric functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11332 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the gradient rearrangement of functions Amato, Vincenzo Gentile, Andrea Nitsch, Carlo Trombetti, Cristina Analysis of PDEs 26A45, 35A23, 35B45 In this paper, we introduce a symmetrization technique for the gradient of a $\BV$ function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an $\text{\emph{L}}^{\text{1}}$ comparison between the function and its symmetrized. Furthermore, we apply this result to obtain Saint-Venant type inequalities for some geometric functionals. |
| title | On the gradient rearrangement of functions |
| topic | Analysis of PDEs 26A45, 35A23, 35B45 |
| url | https://arxiv.org/abs/2302.11332 |