{"paper":{"title":"On the local character of the extension of traces for Sobolev mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen","submitted_at":"2024-12-17T09:28:31Z","abstract_excerpt":"We prove that a mapping $u \\colon \\mathcal{M}'\\to \\mathcal{N}$, where $\\mathcal{M}'$ and $ \\mathcal{N}$ are compact Riemannian manifolds, is the trace of a Sobolev mapping $U \\colon \\mathcal{M}' \\times [0, 1) \\to \\mathcal{N}$ if and only if it is on some open covering of $\\mathcal{M}'$. In the global case where $\\mathcal{M}$ is a compact Riemannian manifold with boundary, this implies that the analytical obstructions to the extension of a mapping $u \\colon \\partial \\mathcal{M}\\to \\mathcal{N}$ to some Sobolev mapping $U \\colon \\mathcal{M} \\to \\mathcal{N}$ are purely local."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12713","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/2412.12713/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"}