{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GJFUP2623E22O3WFZBV2W3RWZ4","short_pith_number":"pith:GJFUP262","schema_version":"1.0","canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","source":{"kind":"arxiv","id":"1107.3228","version":2},"attestation_state":"computed","paper":{"title":"Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adina Ciomaga (CMLA), Cyril Imbert (CEREMADE, DMA), Emmanuel Chasseigne (LMPT), Guy Barles (LMPT)","submitted_at":"2011-07-16T12:58:11Z","abstract_excerpt":"We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the "},"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":"1107.3228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"95515affbbf3187e61c926a2ae7b0614883bbb3c7133e18a2a932f9723b07d86","abstract_canon_sha256":"50692538be668296107c080f0d7adbef23494488caf748bc4749e51554d78f83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:05.217909Z","signature_b64":"qgy9VnBbqEh9zHXy1i/aT4aipAjmx9i5BOKpqL6/ajAex7b1//dN0YyReP7blQ1s4/DJ7MAjkWbXE29GavwdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","last_reissued_at":"2026-05-18T04:05:05.217263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:05.217263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adina Ciomaga (CMLA), Cyril Imbert (CEREMADE, DMA), Emmanuel Chasseigne (LMPT), Guy Barles (LMPT)","submitted_at":"2011-07-16T12:58:11Z","abstract_excerpt":"We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3228","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":"1107.3228","created_at":"2026-05-18T04:05:05.217358+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.3228v2","created_at":"2026-05-18T04:05:05.217358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3228","created_at":"2026-05-18T04:05:05.217358+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJFUP2623E22","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJFUP2623E22O3WF","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJFUP262","created_at":"2026-05-18T12:26:30.835961+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/GJFUP2623E22O3WFZBV2W3RWZ4","json":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4.json","graph_json":"https://pith.science/api/pith-number/GJFUP2623E22O3WFZBV2W3RWZ4/graph.json","events_json":"https://pith.science/api/pith-number/GJFUP2623E22O3WFZBV2W3RWZ4/events.json","paper":"https://pith.science/paper/GJFUP262"},"agent_actions":{"view_html":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4","download_json":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4.json","view_paper":"https://pith.science/paper/GJFUP262","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.3228&json=true","fetch_graph":"https://pith.science/api/pith-number/GJFUP2623E22O3WFZBV2W3RWZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/GJFUP2623E22O3WFZBV2W3RWZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/action/storage_attestation","attest_author":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/action/author_attestation","sign_citation":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/action/citation_signature","submit_replication":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/action/replication_record"}},"created_at":"2026-05-18T04:05:05.217358+00:00","updated_at":"2026-05-18T04:05:05.217358+00:00"}