{"paper":{"title":"The extension of traces for Sobolev mappings between manifolds","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":"2024-03-27T16:27:23Z","abstract_excerpt":"The compact Riemannian manifolds $\\mathcal{M}$ and $\\mathcal{N}$ for which the trace operator from the first-order Sobolev space of mappings $\\smash{\\dot{W}}^{1, p} (\\mathcal{M}, \\mathcal{N})$ to the fractional Sobolev-Slobodecki\\u{\\i} space $\\smash{\\smash{\\dot{W}}^{1 - 1/p, p}} (\\partial \\mathcal{M}, \\mathcal{N})$ is surjective when $1 < p < \\dim \\mathcal{M}$ are characterised. The traces are extended using a new construction which can be carried out assuming the absence of the known topological and analytical obstructions. When $p \\ge \\dim \\mathcal{M}$ the same construction provides a Sobole"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18738","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/2403.18738/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"}