{"paper":{"title":"On Sobolev spaces and density theorems on Finsler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alireza Shahi, Behroz Bidabad","submitted_at":"2013-10-30T05:23:28Z","abstract_excerpt":"Let $(M,F)$ be a $C^\\infty$ Finsler manifold, $p\\geq 1$ a real number, $k$ a positive integer and $H_k^p (M)$ a certain Sobolev space determined by a Finsler structure $F$.\n  Here, it is shown that the set of all real $C^{\\infty}$ functions with compact support on $M$ is dense in the Sobolev space $H_1^p (M)$.\n  This result permits to approximate certain solution of Dirichlet problem living on $H_1^p (M)$ by $C^ \\infty$ functions with compact support on $(M,F)$.\n  Moreover, let $W \\subset M$ be a regular domain with the $C^r$ boundary $\\partial W$, then the set of all real functions in $C^r (W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8027","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"}