{"paper":{"title":"Density of bounded maps in Sobolev spaces into complete manifolds","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":"2015-01-28T15:13:20Z","abstract_excerpt":"Given a complete noncompact Riemannian manifold $N^n$, we investigate whether the set of bounded Sobolev maps $(W^{1, p} \\cap L^\\infty) (Q^m; N^n)$ on the cube $Q^m$ is strongly dense in the Sobolev space $W^{1, p} (Q^m; N^n)$ for $1 \\le p \\le m$. The density always holds when $p$ is not an integer. When $p$ is an integer, the density can fail, and we prove that a quantitative trimming property is equivalent with the density. This new condition is ensured for example by a uniform Lipschitz geometry of $N^n$. As a byproduct, we give necessary and sufficient conditions for the strong density of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07136","kind":"arxiv","version":4},"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"}