{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:AXDBLD6IYUR4WXKGQ6CFZIL5QT","short_pith_number":"pith:AXDBLD6I","schema_version":"1.0","canonical_sha256":"05c6158fc8c523cb5d4687845ca17d84f04ef09fcc417c15e9ca230ffe32ed0c","source":{"kind":"arxiv","id":"1907.02455","version":3},"attestation_state":"computed","paper":{"title":"$C^{2s}$ regularity for fully nonlinear nonlocal equations with bounded right hand side","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hern\\'an Vivas","submitted_at":"2019-07-04T15:28:23Z","abstract_excerpt":"We establish sharp $C^{2s}$ interior regularity estimates for solutions of fully nonlinear nonlocal equations with bounded right hand side. More precisely, we show that if $I$ is a fully nonlinear nonlocal concave or convex elliptic operator and $f\\in L^\\infty(B_1)$ then \\[ Iu=f\\quad\\textrm{ in }\\quad B_1 \\quad \\Rightarrow\\quad u\\in C^{2s}(B_{1/2}). \\] This result generalizes the linear counterpart proved by Ros-Oton and Serra and extends previous available results for fully nonlinear nonlocal operators. As an application, we get a basic regularity estimate for the nonlocal two membranes probl"},"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":"1907.02455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T15:28:23Z","cross_cats_sorted":[],"title_canon_sha256":"568586ca36ecc7c20d5738dc962450fcb92aed96c02962f5bda857b669a2548d","abstract_canon_sha256":"84360ad6bfcb9e035e4f4a8cc4467e28853cbc1e388af015b046aeb5a037aa55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:48.600976Z","signature_b64":"oDYFKIQhSIgkXA8WxFcwgb+SHAMsvGSqkF9oPVpxUhbJil8M1ahTEh8KB5BPH22hltPnc1fSbvlkGGrQt4+HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05c6158fc8c523cb5d4687845ca17d84f04ef09fcc417c15e9ca230ffe32ed0c","last_reissued_at":"2026-05-17T23:40:48.600251Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:48.600251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C^{2s}$ regularity for fully nonlinear nonlocal equations with bounded right hand side","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hern\\'an Vivas","submitted_at":"2019-07-04T15:28:23Z","abstract_excerpt":"We establish sharp $C^{2s}$ interior regularity estimates for solutions of fully nonlinear nonlocal equations with bounded right hand side. More precisely, we show that if $I$ is a fully nonlinear nonlocal concave or convex elliptic operator and $f\\in L^\\infty(B_1)$ then \\[ Iu=f\\quad\\textrm{ in }\\quad B_1 \\quad \\Rightarrow\\quad u\\in C^{2s}(B_{1/2}). \\] This result generalizes the linear counterpart proved by Ros-Oton and Serra and extends previous available results for fully nonlinear nonlocal operators. As an application, we get a basic regularity estimate for the nonlocal two membranes probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02455","kind":"arxiv","version":3},"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":"1907.02455","created_at":"2026-05-17T23:40:48.600370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02455v3","created_at":"2026-05-17T23:40:48.600370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02455","created_at":"2026-05-17T23:40:48.600370+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXDBLD6IYUR4","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXDBLD6IYUR4WXKG","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXDBLD6I","created_at":"2026-05-18T12:33:12.712433+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/AXDBLD6IYUR4WXKGQ6CFZIL5QT","json":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT.json","graph_json":"https://pith.science/api/pith-number/AXDBLD6IYUR4WXKGQ6CFZIL5QT/graph.json","events_json":"https://pith.science/api/pith-number/AXDBLD6IYUR4WXKGQ6CFZIL5QT/events.json","paper":"https://pith.science/paper/AXDBLD6I"},"agent_actions":{"view_html":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT","download_json":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT.json","view_paper":"https://pith.science/paper/AXDBLD6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02455&json=true","fetch_graph":"https://pith.science/api/pith-number/AXDBLD6IYUR4WXKGQ6CFZIL5QT/graph.json","fetch_events":"https://pith.science/api/pith-number/AXDBLD6IYUR4WXKGQ6CFZIL5QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT/action/storage_attestation","attest_author":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT/action/author_attestation","sign_citation":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT/action/citation_signature","submit_replication":"https://pith.science/pith/AXDBLD6IYUR4WXKGQ6CFZIL5QT/action/replication_record"}},"created_at":"2026-05-17T23:40:48.600370+00:00","updated_at":"2026-05-17T23:40:48.600370+00:00"}