{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2U4QCPDVIBBO3SFVHBR7VABEH5","short_pith_number":"pith:2U4QCPDV","schema_version":"1.0","canonical_sha256":"d539013c754042edc8b53863fa80243f70f16fe402b3d0c852a8fb2bf78961b3","source":{"kind":"arxiv","id":"1004.3956","version":2},"attestation_state":"computed","paper":{"title":"Regularity of the extremal solution for some elliptic problems with advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Ye, Feng Zhou, Xue Luo","submitted_at":"2010-04-22T16:20:03Z","abstract_excerpt":"In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\\triangle u+c(x)\\cdot\\nabla u=\\lambda f(u)$ on a bounded smooth domain of $\\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\\in (0, \\infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two."},"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":"1004.3956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-22T16:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"3c744b77aecf71c708da11c2429246b3d9f89dc3551f1ed2cdb423fb5a95029a","abstract_canon_sha256":"a682fe9964bc3081f6dceef6a7bcbb0c2332d2af520a8b68ef647ce946333acd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:04.246332Z","signature_b64":"lV7pPF1XwD2+1MxIz+ONIKkdXVSf/D2KXqBcc3KpNFZbPjRGIMtMcUqRFCfXIaugVrsNZZkxSrjGk5wL2TC1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d539013c754042edc8b53863fa80243f70f16fe402b3d0c852a8fb2bf78961b3","last_reissued_at":"2026-05-18T04:05:04.245538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:04.245538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of the extremal solution for some elliptic problems with advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Ye, Feng Zhou, Xue Luo","submitted_at":"2010-04-22T16:20:03Z","abstract_excerpt":"In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\\triangle u+c(x)\\cdot\\nabla u=\\lambda f(u)$ on a bounded smooth domain of $\\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\\in (0, \\infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3956","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":"1004.3956","created_at":"2026-05-18T04:05:04.245611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.3956v2","created_at":"2026-05-18T04:05:04.245611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3956","created_at":"2026-05-18T04:05:04.245611+00:00"},{"alias_kind":"pith_short_12","alias_value":"2U4QCPDVIBBO","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2U4QCPDVIBBO3SFV","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2U4QCPDV","created_at":"2026-05-18T12:26:03.138858+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/2U4QCPDVIBBO3SFVHBR7VABEH5","json":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5.json","graph_json":"https://pith.science/api/pith-number/2U4QCPDVIBBO3SFVHBR7VABEH5/graph.json","events_json":"https://pith.science/api/pith-number/2U4QCPDVIBBO3SFVHBR7VABEH5/events.json","paper":"https://pith.science/paper/2U4QCPDV"},"agent_actions":{"view_html":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5","download_json":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5.json","view_paper":"https://pith.science/paper/2U4QCPDV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.3956&json=true","fetch_graph":"https://pith.science/api/pith-number/2U4QCPDVIBBO3SFVHBR7VABEH5/graph.json","fetch_events":"https://pith.science/api/pith-number/2U4QCPDVIBBO3SFVHBR7VABEH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5/action/storage_attestation","attest_author":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5/action/author_attestation","sign_citation":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5/action/citation_signature","submit_replication":"https://pith.science/pith/2U4QCPDVIBBO3SFVHBR7VABEH5/action/replication_record"}},"created_at":"2026-05-18T04:05:04.245611+00:00","updated_at":"2026-05-18T04:05:04.245611+00:00"}