{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JNILG4TSZ3K3XPV4JQ7MLR54AN","short_pith_number":"pith:JNILG4TS","schema_version":"1.0","canonical_sha256":"4b50b37272ced5bbbebc4c3ec5c7bc034b4c7591c56b474c09aec908bf496ef2","source":{"kind":"arxiv","id":"1803.10304","version":1},"attestation_state":"computed","paper":{"title":"Boundary regularity for Monge-Amp\\`ere equations with unbounded right hand side","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ovidiu Savin, Qian Zhang","submitted_at":"2018-03-27T20:24:11Z","abstract_excerpt":"We consider Monge-Amp\\`ere equations with right hand side $f$ that degenerate to $\\infty$ near the boundary of a convex domain $\\Omega$, which are of the type $$\\mathrm{det}\\;D^2 u=f\\quad\\mathrm{in}\\;\\Omega,\\quad\\quad f\\sim d^{-\\alpha}_{\\partial\\Omega}\\quad\\mathrm{near}\\;\\partial\\Omega,$$ where $d_{\\partial\\Omega}$ represents the distance to $\\partial \\Omega$ and $-\\alpha$ is a negative power with $\\alpha\\in(0,2)$. We study the boundary regularity of the solutions and establish a localization theorem for boundary sections."},"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":"1803.10304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-27T20:24:11Z","cross_cats_sorted":[],"title_canon_sha256":"116e33d364ff1b24af0d0ec0939fe57e49d5b9720e29e86ba9ae8adc419b7370","abstract_canon_sha256":"997c1c4bb6f2edf2e3b60521b3db0177d6c216902c862535ddaf4a42d7279e25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:55.913242Z","signature_b64":"HMOuPBoP/oB3F5+GR98tqiBmKvBaJPzKfjud0w3qs6t26RfNrzrae7E7bwJF+WL1a+qpin5z4NhxVGKr9CN3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b50b37272ced5bbbebc4c3ec5c7bc034b4c7591c56b474c09aec908bf496ef2","last_reissued_at":"2026-05-18T00:19:55.912554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:55.912554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary regularity for Monge-Amp\\`ere equations with unbounded right hand side","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ovidiu Savin, Qian Zhang","submitted_at":"2018-03-27T20:24:11Z","abstract_excerpt":"We consider Monge-Amp\\`ere equations with right hand side $f$ that degenerate to $\\infty$ near the boundary of a convex domain $\\Omega$, which are of the type $$\\mathrm{det}\\;D^2 u=f\\quad\\mathrm{in}\\;\\Omega,\\quad\\quad f\\sim d^{-\\alpha}_{\\partial\\Omega}\\quad\\mathrm{near}\\;\\partial\\Omega,$$ where $d_{\\partial\\Omega}$ represents the distance to $\\partial \\Omega$ and $-\\alpha$ is a negative power with $\\alpha\\in(0,2)$. We study the boundary regularity of the solutions and establish a localization theorem for boundary sections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10304","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.10304","created_at":"2026-05-18T00:19:55.912646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10304v1","created_at":"2026-05-18T00:19:55.912646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10304","created_at":"2026-05-18T00:19:55.912646+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNILG4TSZ3K3","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNILG4TSZ3K3XPV4","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNILG4TS","created_at":"2026-05-18T12:32:31.084164+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/JNILG4TSZ3K3XPV4JQ7MLR54AN","json":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN.json","graph_json":"https://pith.science/api/pith-number/JNILG4TSZ3K3XPV4JQ7MLR54AN/graph.json","events_json":"https://pith.science/api/pith-number/JNILG4TSZ3K3XPV4JQ7MLR54AN/events.json","paper":"https://pith.science/paper/JNILG4TS"},"agent_actions":{"view_html":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN","download_json":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN.json","view_paper":"https://pith.science/paper/JNILG4TS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10304&json=true","fetch_graph":"https://pith.science/api/pith-number/JNILG4TSZ3K3XPV4JQ7MLR54AN/graph.json","fetch_events":"https://pith.science/api/pith-number/JNILG4TSZ3K3XPV4JQ7MLR54AN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN/action/storage_attestation","attest_author":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN/action/author_attestation","sign_citation":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN/action/citation_signature","submit_replication":"https://pith.science/pith/JNILG4TSZ3K3XPV4JQ7MLR54AN/action/replication_record"}},"created_at":"2026-05-18T00:19:55.912646+00:00","updated_at":"2026-05-18T00:19:55.912646+00:00"}