{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7BO6M46UG3PQJYELYTAFKZBPPZ","short_pith_number":"pith:7BO6M46U","schema_version":"1.0","canonical_sha256":"f85de673d436df04e08bc4c055642f7e671d006093c2af617f74afdaed577e3d","source":{"kind":"arxiv","id":"2407.20385","version":3},"attestation_state":"computed","paper":{"title":"Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mihalis Mourgoglou, Xavier Tolsa","submitted_at":"2024-07-29T19:21:50Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{n+1}$ be a bounded chord-arc domain, let $\\mathcal L=-{\\rm div} A\\nabla$ be an elliptic operator in $\\Omega$ associated with a matrix $A$ having Dini mean oscillation coefficients, and let $1<p\\leq 2$. In this paper we show that if the regularity problem for $\\mathcal L$ is solvable in $L^q$ for some $q>p$ in $\\Omega$, $\\partial \\Omega$ supports a weak $p$-Poincar\\'e inequality, and $\\Omega$ has very big pieces of superdomains for which the Neumann problem for $\\mathcal L$ is solvable uniformly in $L^q$, then the Neumann problem for $\\mathcal L$ is solvable in $"},"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":"2407.20385","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T19:21:50Z","cross_cats_sorted":[],"title_canon_sha256":"35974e4cb521e039a61b00eef6dbbfddbf491c6792ebd0c6457c2c949f0014ab","abstract_canon_sha256":"1e4344979823a4014237b7719d78ff5bf2cb834a84233470fb806e73fca06f30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:32:11.202136Z","signature_b64":"5sG/HrjxtX3QGXK05KwpotAVvX8hJ7jR884Y/DT6aLxxyf6zO0+GrpmNNM6FNTSWuAkjPQbV2d25HHpKmVEzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f85de673d436df04e08bc4c055642f7e671d006093c2af617f74afdaed577e3d","last_reissued_at":"2026-07-05T09:32:11.201648Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:32:11.201648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mihalis Mourgoglou, Xavier Tolsa","submitted_at":"2024-07-29T19:21:50Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{n+1}$ be a bounded chord-arc domain, let $\\mathcal L=-{\\rm div} A\\nabla$ be an elliptic operator in $\\Omega$ associated with a matrix $A$ having Dini mean oscillation coefficients, and let $1<p\\leq 2$. In this paper we show that if the regularity problem for $\\mathcal L$ is solvable in $L^q$ for some $q>p$ in $\\Omega$, $\\partial \\Omega$ supports a weak $p$-Poincar\\'e inequality, and $\\Omega$ has very big pieces of superdomains for which the Neumann problem for $\\mathcal L$ is solvable uniformly in $L^q$, then the Neumann problem for $\\mathcal L$ is solvable in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20385","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.20385/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":"2407.20385","created_at":"2026-07-05T09:32:11.201703+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.20385v3","created_at":"2026-07-05T09:32:11.201703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20385","created_at":"2026-07-05T09:32:11.201703+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BO6M46UG3PQ","created_at":"2026-07-05T09:32:11.201703+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BO6M46UG3PQJYEL","created_at":"2026-07-05T09:32:11.201703+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BO6M46U","created_at":"2026-07-05T09:32:11.201703+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13168","citing_title":"Robin Green Function Estimates and a Model of Mammalian Lungs","ref_index":42,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ","json":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ.json","graph_json":"https://pith.science/api/pith-number/7BO6M46UG3PQJYELYTAFKZBPPZ/graph.json","events_json":"https://pith.science/api/pith-number/7BO6M46UG3PQJYELYTAFKZBPPZ/events.json","paper":"https://pith.science/paper/7BO6M46U"},"agent_actions":{"view_html":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ","download_json":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ.json","view_paper":"https://pith.science/paper/7BO6M46U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.20385&json=true","fetch_graph":"https://pith.science/api/pith-number/7BO6M46UG3PQJYELYTAFKZBPPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/7BO6M46UG3PQJYELYTAFKZBPPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ/action/storage_attestation","attest_author":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ/action/author_attestation","sign_citation":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ/action/citation_signature","submit_replication":"https://pith.science/pith/7BO6M46UG3PQJYELYTAFKZBPPZ/action/replication_record"}},"created_at":"2026-07-05T09:32:11.201703+00:00","updated_at":"2026-07-05T09:32:11.201703+00:00"}