{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WHD2SMLRYMZFTDUJ6OQD5N5CTE","short_pith_number":"pith:WHD2SMLR","schema_version":"1.0","canonical_sha256":"b1c7a93171c332598e89f3a03eb7a2993335e0e69cf7f4a32e0e75a12c03a6eb","source":{"kind":"arxiv","id":"1806.00423","version":1},"attestation_state":"computed","paper":{"title":"Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karthik Adimurthi, Nguyen Cong Phuc, Tadele Mengesha","submitted_at":"2018-06-01T16:22:16Z","abstract_excerpt":"Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz domain $\\Omega$. The gradient estimates are obtained in weighted Lebesgue and Lorentz spaces, which also yield estimates in Lorentz-Morrey spaces as well as H\\\"older continuity of solutions. The significance of the work lies on its applicability to very weak solutions (that belong to $W^{1,p}_{0}(\\Omega)$ for some $p>1$ but not necessarily in $W^{1,2}_{0}(\\Omega)$) to inhomogeneous equations with c"},"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":"1806.00423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-01T16:22:16Z","cross_cats_sorted":[],"title_canon_sha256":"06f167538b1d4c5801a93374e40394a6443c8dedd254cd95a7dc45b03b86728b","abstract_canon_sha256":"9d9ccbf1257aa8cf39386bdee3a2fc2dbdb485b82faa761f709d60bed9cfefb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:23.717269Z","signature_b64":"VQHvkfeJT8Zlpo+8yYfkEV7UDe11YSfx8Qvj10authnolBIBMuMd50CWexg98L1thyI9Dts4ieK7TQ85UdAyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1c7a93171c332598e89f3a03eb7a2993335e0e69cf7f4a32e0e75a12c03a6eb","last_reissued_at":"2026-05-18T00:14:23.716756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:23.716756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karthik Adimurthi, Nguyen Cong Phuc, Tadele Mengesha","submitted_at":"2018-06-01T16:22:16Z","abstract_excerpt":"Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz domain $\\Omega$. The gradient estimates are obtained in weighted Lebesgue and Lorentz spaces, which also yield estimates in Lorentz-Morrey spaces as well as H\\\"older continuity of solutions. The significance of the work lies on its applicability to very weak solutions (that belong to $W^{1,p}_{0}(\\Omega)$ for some $p>1$ but not necessarily in $W^{1,2}_{0}(\\Omega)$) to inhomogeneous equations with c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00423","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":"1806.00423","created_at":"2026-05-18T00:14:23.716837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.00423v1","created_at":"2026-05-18T00:14:23.716837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00423","created_at":"2026-05-18T00:14:23.716837+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHD2SMLRYMZF","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHD2SMLRYMZFTDUJ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHD2SMLR","created_at":"2026-05-18T12:32:59.047623+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/WHD2SMLRYMZFTDUJ6OQD5N5CTE","json":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE.json","graph_json":"https://pith.science/api/pith-number/WHD2SMLRYMZFTDUJ6OQD5N5CTE/graph.json","events_json":"https://pith.science/api/pith-number/WHD2SMLRYMZFTDUJ6OQD5N5CTE/events.json","paper":"https://pith.science/paper/WHD2SMLR"},"agent_actions":{"view_html":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE","download_json":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE.json","view_paper":"https://pith.science/paper/WHD2SMLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.00423&json=true","fetch_graph":"https://pith.science/api/pith-number/WHD2SMLRYMZFTDUJ6OQD5N5CTE/graph.json","fetch_events":"https://pith.science/api/pith-number/WHD2SMLRYMZFTDUJ6OQD5N5CTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE/action/storage_attestation","attest_author":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE/action/author_attestation","sign_citation":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE/action/citation_signature","submit_replication":"https://pith.science/pith/WHD2SMLRYMZFTDUJ6OQD5N5CTE/action/replication_record"}},"created_at":"2026-05-18T00:14:23.716837+00:00","updated_at":"2026-05-18T00:14:23.716837+00:00"}