{"paper":{"title":"Anisotropic gradient rearrangement of BV functions and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gloria Paoli, Yabo Yang","submitted_at":"2026-05-15T11:01:39Z","abstract_excerpt":"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\n  derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15849","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15849/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.708746Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.825039Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"42728cf14a41703be5a60578e6b8907c8fce5703e1fc2dbcac3796b493165050"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}