{"paper":{"title":"Weak regularity of the inverse under minimal assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.CA","authors_text":"Aapo Kauranen, Rami Luisto, Stanislav Hencl","submitted_at":"2018-04-10T10:58:38Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^3$ be a domain and let $f\\in BV_{\\operatorname{loc}}(\\Omega,\\mathbb{R}^3)$ be a homeomorphism such that its distributional adjugate is a finite Radon measure. We show that its inverse has bounded variation $f^{-1}\\in BV_{\\operatorname{loc}}$. The condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03449","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}