{"paper":{"title":"The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with 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":"2018-10-16T11:19:27Z","abstract_excerpt":"Let $M$ be a smooth manifold with boundary $\\partial M$ and bounded geometry, $\\partial_D M \\subset \\partial M$ be an open and closed subset, $P$ be a second order differential operator on $M$, and $b$ be a first order differential operator on $\\partial M \\smallsetminus \\partial_D M$. We prove the regularity and well-posedness of the mixed Robin boundary value problem $$Pu = f \\mbox{ in } M,\\ u = 0 \\mbox{ on } \\partial_D M,\\ \\partial^P_\\nu u + bu = 0 \\mbox{ on } \\partial M \\setminus \\partial_D M$$ under some natural assumptions. Our operators act on sections of a vector bundle $E \\to M$ with b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06926","kind":"arxiv","version":2},"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"}