{"paper":{"title":"A new obstruction to the extension problem for Sobolev maps between manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fabrice Bethuel","submitted_at":"2014-02-19T10:26:03Z","abstract_excerpt":"The main result of the present paper, combined with earlier results of Hardt and Lin settles the extension problem for $W^{1,p}(\\mathcal M, \\mathcal N)$, where $\\mathcal M$ and $\\mathcal N$ are compact riemannian manfolds, $\\mathcal M$ having non-empty smooth boundary and assuming moreover that $\\mathcal N$ is simply connected. The main question which is studied is the following: Given a map in the trace space $W^{1-\\frac{1}{p}, p} (\\partial \\mathcal M, \\mathcal N)$, does it possess an extension in $W^{1,p}(\\mathcal M, \\mathcal N)$? We show that the answer is negative in the case $\\mathfrak p_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4614","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":""},"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"}