{"paper":{"title":"Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Jean Van Schaftingen, Mircea Petrache","submitted_at":"2015-08-31T13:16:37Z","abstract_excerpt":"Given $n \\in \\mathbb{N}_*$, a compact Riemannian manifold $M$ and a Sobolev map $u \\in W^{n/(n + 1), n + 1} (\\mathbb{S}^n; M)$, we construct a map $U$ in the Sobolev-Marcinkiewicz (or Lorentz-Sobolev) space $W^{1, (n + 1, \\infty)} (\\mathbb{B}^{n + 1}; M)$ such that $u = U$ in the sense of traces on $\\mathbb{S}^{n} = \\partial \\mathbb{B}^{n + 1}$ and whose derivative is controlled: for every $\\lambda > 0$, $$ \\lambda^{n + 1} \\big\\vert\\big\\{ x \\in \\mathbb{B}^{n + 1} : \\vert D U (x)\\vert > \\lambda\\big\\}\\big\\vert\n  \\le \\gamma \\Big(\\int_{\\mathbb{S}^n}\\int_{\\mathbb{S}^n} \\frac{\\vert u (y) - u (z)\\ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07813","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"}