{"paper":{"title":"Strong approximation of fractional Sobolev maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Augusto C. Ponce, Jean Van Schaftingen, Pierre Bousquet","submitted_at":"2013-10-22T19:25:57Z","abstract_excerpt":"Brezis and Mironescu have announced several years ago that for a compact manifold $N^n \\subset \\mathbb{R}^\\nu$ and for real numbers $0 < s < 1$ and $1 \\le p < \\infty$ the class $C^\\infty(\\overline{Q}^m; N^n)$ of smooth maps on the cube with values into $N^n$ is dense with respect to the strong topology in the Sobolev space $W^{s, p}(Q^m; N^n)$ when the homotopy group $\\pi_{\\lfloor sp \\rfloor}(N^n)$ of order $\\lfloor sp \\rfloor$ is trivial. The proof of this beautiful result is long and rather involved. Under the additional assumption that $N^n$ is $\\lfloor sp \\rfloor$ simply connected, we give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6017","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"}