{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:MMAYVE4Q62OYCUBFGSGE34ZCNY","short_pith_number":"pith:MMAYVE4Q","schema_version":"1.0","canonical_sha256":"63018a9390f69d815025348c4df3226e3838544871b4c2429aef8b2b826e1d88","source":{"kind":"arxiv","id":"2207.13504","version":2},"attestation_state":"computed","paper":{"title":"The exterior Dirichlet problem for the homogeneous $k$-Hessian equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dekai Zhang, Xi-Nan Ma","submitted_at":"2022-07-27T13:15:16Z","abstract_excerpt":"We study the exterior Dirichlet problem for the homogeneous $k$-Hessian equation. The prescribed asymptotic behavior at infinity of the solution is zero if $k<\\frac{n}{2}$, it is $\\log|x|+O(1)$ if $k=\\frac{n}{2}$ and it is $|x|^{\\frac{2k-n}{n}}+O(1)$ if $k>\\frac{n}{2}$. By constructing smooth solutions of approximating non-degenerate $k$-Hessian equations with uniform $C^{1,1}$-estimates, we prove the existence part. The uniqueness follows from the comparison theorem and thus the $C^{1,1}$ regularity of the solution of the homogeneous $k$-Hessian equation in the exterior domain is proved. We a"},"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":"2207.13504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-27T13:15:16Z","cross_cats_sorted":[],"title_canon_sha256":"216f887a1e66362b13f02f213394c40c15d38dbfddbe06b25d73aaac0948ddbe","abstract_canon_sha256":"202c396293a4d9770bfb021d8b1bed45a70b039f3e8e3b3c0dda18622ec84332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:11.167736Z","signature_b64":"2gp+3X4H+xVJttu1YTiLih3m6wkrkFC0cwtkZ0fFrWvD2fA+nD8ndpM9yZ7v7MOTVwYvKE8dodHsVj3HmBWoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63018a9390f69d815025348c4df3226e3838544871b4c2429aef8b2b826e1d88","last_reissued_at":"2026-07-05T08:10:11.167323Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:11.167323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The exterior Dirichlet problem for the homogeneous $k$-Hessian equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dekai Zhang, Xi-Nan Ma","submitted_at":"2022-07-27T13:15:16Z","abstract_excerpt":"We study the exterior Dirichlet problem for the homogeneous $k$-Hessian equation. The prescribed asymptotic behavior at infinity of the solution is zero if $k<\\frac{n}{2}$, it is $\\log|x|+O(1)$ if $k=\\frac{n}{2}$ and it is $|x|^{\\frac{2k-n}{n}}+O(1)$ if $k>\\frac{n}{2}$. By constructing smooth solutions of approximating non-degenerate $k$-Hessian equations with uniform $C^{1,1}$-estimates, we prove the existence part. The uniqueness follows from the comparison theorem and thus the $C^{1,1}$ regularity of the solution of the homogeneous $k$-Hessian equation in the exterior domain is proved. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.13504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.13504/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2207.13504","created_at":"2026-07-05T08:10:11.167389+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.13504v2","created_at":"2026-07-05T08:10:11.167389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.13504","created_at":"2026-07-05T08:10:11.167389+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMAYVE4Q62OY","created_at":"2026-07-05T08:10:11.167389+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMAYVE4Q62OYCUBF","created_at":"2026-07-05T08:10:11.167389+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMAYVE4Q","created_at":"2026-07-05T08:10:11.167389+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04422","citing_title":"Optimal Rigidity and Classification Results for the $k$-Hessian Equation of Lane--Emden Type","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY","json":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY.json","graph_json":"https://pith.science/api/pith-number/MMAYVE4Q62OYCUBFGSGE34ZCNY/graph.json","events_json":"https://pith.science/api/pith-number/MMAYVE4Q62OYCUBFGSGE34ZCNY/events.json","paper":"https://pith.science/paper/MMAYVE4Q"},"agent_actions":{"view_html":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY","download_json":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY.json","view_paper":"https://pith.science/paper/MMAYVE4Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.13504&json=true","fetch_graph":"https://pith.science/api/pith-number/MMAYVE4Q62OYCUBFGSGE34ZCNY/graph.json","fetch_events":"https://pith.science/api/pith-number/MMAYVE4Q62OYCUBFGSGE34ZCNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY/action/storage_attestation","attest_author":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY/action/author_attestation","sign_citation":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY/action/citation_signature","submit_replication":"https://pith.science/pith/MMAYVE4Q62OYCUBFGSGE34ZCNY/action/replication_record"}},"created_at":"2026-07-05T08:10:11.167389+00:00","updated_at":"2026-07-05T08:10:11.167389+00:00"}