{"paper":{"title":"Global invertibility of Sobolev mappings with prescribed homeomorphic boundary values","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Sabrina Traver (Syracuse University)","submitted_at":"2025-07-09T18:29:55Z","abstract_excerpt":"Let $X, Y \\subset \\mathbb{R}^n$ be Lipschitz domains, and suppose there is a homeomorphism $\\varphi \\colon \\overline{X} \\to \\overline{Y}$. We consider the class of Sobolev mappings $f \\in W^{1,n} (X, \\mathbb{R}^n)$ with a strictly positive Jacobian determinant almost everywhere, whose Sobolev trace coincides with $\\varphi$ on $\\partial X$. We prove that every mapping in this class extends continuously to $\\overline{X}$ and is a monotone (continuous) surjection from $\\overline{X}$ onto $\\overline{Y}$ in the sense of C.B. Morrey. As monotone mappings, they may squeeze but not fold the reference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07206","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07206/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}