{"paper":{"title":"$\\mathsf{L}^1$-elliptic regularity and $H=W$ on the whole $\\mathsf{L}^p$-scale on arbitrary manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Batu G\\\"uneysu, Davide Guidetti, Diego Pallara","submitted_at":"2014-05-12T07:50:59Z","abstract_excerpt":"We define abstract Sobolev type spaces on $\\mathsf{L}^p$-scales, $p\\in [1,\\infty)$, on Hermitian vector bundles over possibly noncompact manifolds, which are induced by smooth measures and families $\\mathfrak{P}$ of linear partial differential operators, and we prove the density of the corresponding smooth Sobolev sections in these spaces under a generalized ellipticity condition on the underlying family. In particular, this implies a covariant version of Meyers-Serrin\\rq{}s theorem on the whole $\\mathsf{L}^p$-scale, for arbitrary Riemannian manifolds. Furthermore, we prove a new local ellipti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2654","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"}