{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:E75PNTQ2BLRLUL4IQ36N3LMZAN","short_pith_number":"pith:E75PNTQ2","schema_version":"1.0","canonical_sha256":"27faf6ce1a0ae2ba2f8886fcddad9903501cc6fcebd9dd5e607cf53beab99d2b","source":{"kind":"arxiv","id":"1810.06926","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.06926","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-16T11:19:27Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4c6de4f0a9124ba5502d2cc8e6e7ba57662787e5afb2531346378df9b3cbc543","abstract_canon_sha256":"ae159e1c89bf86e48f65ff1f7abfc3cc0fb3150086430cc681c0ec282307fe2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:45.516492Z","signature_b64":"RG9sodve0rDnMijpOtKscdtwqkhabvdAK2r9P+16e4W+Hff2TQpTw+yhSk+uUOObSYzukMzLyFGKNyJnzmoeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27faf6ce1a0ae2ba2f8886fcddad9903501cc6fcebd9dd5e607cf53beab99d2b","last_reissued_at":"2026-05-17T23:48:45.515981Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:45.515981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.06926","created_at":"2026-05-17T23:48:45.516071+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.06926v2","created_at":"2026-05-17T23:48:45.516071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06926","created_at":"2026-05-17T23:48:45.516071+00:00"},{"alias_kind":"pith_short_12","alias_value":"E75PNTQ2BLRL","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"E75PNTQ2BLRLUL4I","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"E75PNTQ2","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN","json":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN.json","graph_json":"https://pith.science/api/pith-number/E75PNTQ2BLRLUL4IQ36N3LMZAN/graph.json","events_json":"https://pith.science/api/pith-number/E75PNTQ2BLRLUL4IQ36N3LMZAN/events.json","paper":"https://pith.science/paper/E75PNTQ2"},"agent_actions":{"view_html":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN","download_json":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN.json","view_paper":"https://pith.science/paper/E75PNTQ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.06926&json=true","fetch_graph":"https://pith.science/api/pith-number/E75PNTQ2BLRLUL4IQ36N3LMZAN/graph.json","fetch_events":"https://pith.science/api/pith-number/E75PNTQ2BLRLUL4IQ36N3LMZAN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN/action/storage_attestation","attest_author":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN/action/author_attestation","sign_citation":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN/action/citation_signature","submit_replication":"https://pith.science/pith/E75PNTQ2BLRLUL4IQ36N3LMZAN/action/replication_record"}},"created_at":"2026-05-17T23:48:45.516071+00:00","updated_at":"2026-05-17T23:48:45.516071+00:00"}