{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:7QEWHFGC6G4YYXOZ2SHJGDPWHW","short_pith_number":"pith:7QEWHFGC","schema_version":"1.0","canonical_sha256":"fc096394c2f1b98c5dd9d48e930df63d9fd6351685ce46ec7befe889591670c2","source":{"kind":"arxiv","id":"0906.5285","version":1},"attestation_state":"computed","paper":{"title":"Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Robin Nittka","submitted_at":"2009-06-29T14:55:13Z","abstract_excerpt":"For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in particular with Neumann boundary conditions are Hoelder continuous for sufficiently $L^p$-regular right-hand sides. From this we deduce that the parabolic problem with Robin or Wentzell-Robin boundary conditions are well-posed on $\\mathrm{C}(\\bar{\\Omega})$."},"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":"0906.5285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-29T14:55:13Z","cross_cats_sorted":[],"title_canon_sha256":"c830133b7d816fa0de10c39ae2b9f75d1c861c3b09ccdd0cdf957d31cfca4ea7","abstract_canon_sha256":"1e5a5e002cca75dc735075fd43f1a33bf59382dfe47a7088bb6758cf7a378025"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:36.008899Z","signature_b64":"s7Zs2/0cREIg/wdKW6Xlx3/ctEE/LcSlP/q91zT04szXaKKfDN1Fc1AFjtAfpABtYXZlT6m4bt8yzh8LDY+dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc096394c2f1b98c5dd9d48e930df63d9fd6351685ce46ec7befe889591670c2","last_reissued_at":"2026-05-18T04:20:36.008139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:36.008139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Robin Nittka","submitted_at":"2009-06-29T14:55:13Z","abstract_excerpt":"For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in particular with Neumann boundary conditions are Hoelder continuous for sufficiently $L^p$-regular right-hand sides. From this we deduce that the parabolic problem with Robin or Wentzell-Robin boundary conditions are well-posed on $\\mathrm{C}(\\bar{\\Omega})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5285","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":"0906.5285","created_at":"2026-05-18T04:20:36.008244+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.5285v1","created_at":"2026-05-18T04:20:36.008244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5285","created_at":"2026-05-18T04:20:36.008244+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QEWHFGC6G4Y","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QEWHFGC6G4YYXOZ","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QEWHFGC","created_at":"2026-05-18T12:25:58.837520+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/7QEWHFGC6G4YYXOZ2SHJGDPWHW","json":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW.json","graph_json":"https://pith.science/api/pith-number/7QEWHFGC6G4YYXOZ2SHJGDPWHW/graph.json","events_json":"https://pith.science/api/pith-number/7QEWHFGC6G4YYXOZ2SHJGDPWHW/events.json","paper":"https://pith.science/paper/7QEWHFGC"},"agent_actions":{"view_html":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW","download_json":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW.json","view_paper":"https://pith.science/paper/7QEWHFGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.5285&json=true","fetch_graph":"https://pith.science/api/pith-number/7QEWHFGC6G4YYXOZ2SHJGDPWHW/graph.json","fetch_events":"https://pith.science/api/pith-number/7QEWHFGC6G4YYXOZ2SHJGDPWHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW/action/storage_attestation","attest_author":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW/action/author_attestation","sign_citation":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW/action/citation_signature","submit_replication":"https://pith.science/pith/7QEWHFGC6G4YYXOZ2SHJGDPWHW/action/replication_record"}},"created_at":"2026-05-18T04:20:36.008244+00:00","updated_at":"2026-05-18T04:20:36.008244+00:00"}