{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZZW673T4V33B7XNHDENBIKX5GY","short_pith_number":"pith:ZZW673T4","schema_version":"1.0","canonical_sha256":"ce6defee7caef61fdda7191a142afd3623a789f2094db04bcdb7e1404e17ce07","source":{"kind":"arxiv","id":"1311.4783","version":1},"attestation_state":"computed","paper":{"title":"The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\\infty$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew J. Morris, Marius Mitrea, Steve Hofmann","submitted_at":"2013-11-19T15:40:55Z","abstract_excerpt":"We consider layer potentials associated to elliptic operators $Lu=-{\\rm div}(A \\nabla u)$ acting in the upper half-space $\\mathbb{R}^{n+1}_+$ for $n\\geq 2$, or more generally, in a Lipschitz graph domain, where the coefficient matrix $A$ is $L^\\infty$ and $t$-independent, and solutions of $Lu=0$ satisfy interior estimates of De Giorgi/Nash/Moser type. A \"Calder\\'on-Zygmund\" theory is developed for the boundedness of layer potentials, whereby sharp $L^p$ and endpoint space bounds are deduced from $L^2$ bounds. Appropriate versions of the classical \"jump-relation\" formulae are also derived. 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":"1311.4783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T15:40:55Z","cross_cats_sorted":[],"title_canon_sha256":"9feabf14f54310c17a50ec87a9ea26bb3a2e7ae573a1cc454281a2dec6cfe0f5","abstract_canon_sha256":"c7cf4413d23da1b11500f6f11085ab806dcf2da7091c7135f35240e05f6e2a58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.336188Z","signature_b64":"b6z/Ndxy7KxAivd11Wgt1IlbjKlMLfuI4Y5uFvdehxMGju2llCAP6c5dtHsYvF836tDEDoUbIeC5IbEjDEj6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce6defee7caef61fdda7191a142afd3623a789f2094db04bcdb7e1404e17ce07","last_reissued_at":"2026-05-18T00:44:29.335553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.335553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\\infty$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew J. Morris, Marius Mitrea, Steve Hofmann","submitted_at":"2013-11-19T15:40:55Z","abstract_excerpt":"We consider layer potentials associated to elliptic operators $Lu=-{\\rm div}(A \\nabla u)$ acting in the upper half-space $\\mathbb{R}^{n+1}_+$ for $n\\geq 2$, or more generally, in a Lipschitz graph domain, where the coefficient matrix $A$ is $L^\\infty$ and $t$-independent, and solutions of $Lu=0$ satisfy interior estimates of De Giorgi/Nash/Moser type. A \"Calder\\'on-Zygmund\" theory is developed for the boundedness of layer potentials, whereby sharp $L^p$ and endpoint space bounds are deduced from $L^2$ bounds. Appropriate versions of the classical \"jump-relation\" formulae are also derived. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4783","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":"1311.4783","created_at":"2026-05-18T00:44:29.335652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4783v1","created_at":"2026-05-18T00:44:29.335652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4783","created_at":"2026-05-18T00:44:29.335652+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZW673T4V33B","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZW673T4V33B7XNH","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZW673T4","created_at":"2026-05-18T12:28:09.283467+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/ZZW673T4V33B7XNHDENBIKX5GY","json":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY.json","graph_json":"https://pith.science/api/pith-number/ZZW673T4V33B7XNHDENBIKX5GY/graph.json","events_json":"https://pith.science/api/pith-number/ZZW673T4V33B7XNHDENBIKX5GY/events.json","paper":"https://pith.science/paper/ZZW673T4"},"agent_actions":{"view_html":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY","download_json":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY.json","view_paper":"https://pith.science/paper/ZZW673T4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4783&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZW673T4V33B7XNHDENBIKX5GY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZW673T4V33B7XNHDENBIKX5GY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY/action/storage_attestation","attest_author":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY/action/author_attestation","sign_citation":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY/action/citation_signature","submit_replication":"https://pith.science/pith/ZZW673T4V33B7XNHDENBIKX5GY/action/replication_record"}},"created_at":"2026-05-18T00:44:29.335652+00:00","updated_at":"2026-05-18T00:44:29.335652+00:00"}