{"paper":{"title":"Well-posedness of the Laplacian on manifolds with boundary and bounded geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Bernd Ammann, Nadine Gro{\\ss}e, Victor Nistor","submitted_at":"2016-11-01T15:54:19Z","abstract_excerpt":"Let $M$ be a Riemannian manifold with a smooth boundary. The main question we address in this article is: \"When is the Laplace-Beltrami operator $\\Delta\\colon H^{k+1}(M)\\cap H^1_0(M) \\to H^{k-1}(M)$, $k\\in \\mathbb{N}_0$, invertible?\" We consider also the case of mixed boundary conditions. The study of this main question leads us to the class of manifolds with boundary and bounded geometry introduced by Schick (Math. Nach. 2001). We begin with some needed results on the geometry of manifolds with boundary and bounded geometry. Let $\\partial_D M \\subset \\partial M$ be an open and closed subset o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00281","kind":"arxiv","version":3},"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"}