{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2FTW5QQ4AZHFIERVLZ4UQDVPOZ","short_pith_number":"pith:2FTW5QQ4","schema_version":"1.0","canonical_sha256":"d1676ec21c064e5412355e79480eaf7651af3dd041b583077d9b00d7c6798bfe","source":{"kind":"arxiv","id":"1211.4180","version":1},"attestation_state":"computed","paper":{"title":"A priori bounds for a class of semi-linear degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genggeng Huang","submitted_at":"2012-11-18T01:15:46Z","abstract_excerpt":"In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\\label{000} a^{ij}(x)\\partial_{ij}u+b^i(x)\\partial_i u +f(x,u)=0,\\text{in}\\Omega\\subset\\subset R^n, {equation} where $a^{ij}\\partial_i \\phi\\partial_j \\phi=0$ on $\\partial \\Omega$, $\\phi$ is the defining function of $\\partial \\Omega$. Imposing suitable conditions on the coefficients and $f(x,u)$, one can get the $L^\\infty$-estimates of \\eqref{000} via blow up method."},"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":"1211.4180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-18T01:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"331578726e46b8dca864efa4962d2ad4ffa9e304939b9ec89f44b7afd0eb9376","abstract_canon_sha256":"713523fdd28b43d29a9f39cf72be5b7c11ab2db91401e39d55a1c2a7907b4198"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:27.737899Z","signature_b64":"YoSMSEzDrYiKrzBAGOoEmAbEgmZV++BxgN5tidK3Zkzedk1j7IpiSWrDfnHm+aSkNryBYc4Xy8raszp3jSliAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1676ec21c064e5412355e79480eaf7651af3dd041b583077d9b00d7c6798bfe","last_reissued_at":"2026-05-18T03:40:27.737198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:27.737198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A priori bounds for a class of semi-linear degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genggeng Huang","submitted_at":"2012-11-18T01:15:46Z","abstract_excerpt":"In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\\label{000} a^{ij}(x)\\partial_{ij}u+b^i(x)\\partial_i u +f(x,u)=0,\\text{in}\\Omega\\subset\\subset R^n, {equation} where $a^{ij}\\partial_i \\phi\\partial_j \\phi=0$ on $\\partial \\Omega$, $\\phi$ is the defining function of $\\partial \\Omega$. Imposing suitable conditions on the coefficients and $f(x,u)$, one can get the $L^\\infty$-estimates of \\eqref{000} via blow up method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4180","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":"1211.4180","created_at":"2026-05-18T03:40:27.737294+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4180v1","created_at":"2026-05-18T03:40:27.737294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4180","created_at":"2026-05-18T03:40:27.737294+00:00"},{"alias_kind":"pith_short_12","alias_value":"2FTW5QQ4AZHF","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2FTW5QQ4AZHFIERV","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2FTW5QQ4","created_at":"2026-05-18T12:26:50.516681+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/2FTW5QQ4AZHFIERVLZ4UQDVPOZ","json":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ.json","graph_json":"https://pith.science/api/pith-number/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/graph.json","events_json":"https://pith.science/api/pith-number/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/events.json","paper":"https://pith.science/paper/2FTW5QQ4"},"agent_actions":{"view_html":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ","download_json":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ.json","view_paper":"https://pith.science/paper/2FTW5QQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4180&json=true","fetch_graph":"https://pith.science/api/pith-number/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/action/storage_attestation","attest_author":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/action/author_attestation","sign_citation":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/action/citation_signature","submit_replication":"https://pith.science/pith/2FTW5QQ4AZHFIERVLZ4UQDVPOZ/action/replication_record"}},"created_at":"2026-05-18T03:40:27.737294+00:00","updated_at":"2026-05-18T03:40:27.737294+00:00"}