Anisotropic gradient rearrangement of BV functions and applications

Fuente: arXiv
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Main Authors: Paoli, Gloria, Yang, Yabo
Format: Preprint
Published: 2026
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_version_ 1866910223675949056
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
id 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