{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:UKPATXQ5RJA4R2WD5CC7R45E6J","short_pith_number":"pith:UKPATXQ5","schema_version":"1.0","canonical_sha256":"a29e09de1d8a41c8eac3e885f8f3a4f26f7cf4a0dcf6bc6f62d8f897f723928c","source":{"kind":"arxiv","id":"2308.05559","version":1},"attestation_state":"computed","paper":{"title":"On higher integrability for $p(x)$-Laplacian equations with drift","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baisheng Yan, Bin Guo, Jingya Chen","submitted_at":"2023-08-10T13:19:35Z","abstract_excerpt":"In this paper, we study the higher integrability for the gradient of weak solutions of $p(x)$-Laplacians equation with drift terms. We prove a version of generalized Gehring's lemma under some weaker condition on the modulus of continuity of variable exponent $p(x)$ and present a modified version of Sobolev-Poincar\\'{e} inequality with such an exponent. When $p(x)>2$ we derive the reverse H\\\"older inequality with a proper dependence on the drift and force terms and establish a specific high integrability result. Our condition on the exponent $p(x)$ is more specific and weaker than the known co"},"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":"2308.05559","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-08-10T13:19:35Z","cross_cats_sorted":[],"title_canon_sha256":"bed33d064caafe2e88b98986d957eb76e90a931b9d655e818428d93ff1a238b7","abstract_canon_sha256":"4b9aea0f2c3d21bea23569bb225952a3946169c9e5cb2e8b1f9de62a3dd586ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:02.351041Z","signature_b64":"owuVxPzToLuCGohjciQ8+QfwroWY57oJtBVZj1iEUv1DRgREzZAopkJbAfH87usYgFqPT5TMHVGOqrulAbohAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29e09de1d8a41c8eac3e885f8f3a4f26f7cf4a0dcf6bc6f62d8f897f723928c","last_reissued_at":"2026-07-05T06:40:02.350514Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:02.350514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On higher integrability for $p(x)$-Laplacian equations with drift","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baisheng Yan, Bin Guo, Jingya Chen","submitted_at":"2023-08-10T13:19:35Z","abstract_excerpt":"In this paper, we study the higher integrability for the gradient of weak solutions of $p(x)$-Laplacians equation with drift terms. We prove a version of generalized Gehring's lemma under some weaker condition on the modulus of continuity of variable exponent $p(x)$ and present a modified version of Sobolev-Poincar\\'{e} inequality with such an exponent. When $p(x)>2$ we derive the reverse H\\\"older inequality with a proper dependence on the drift and force terms and establish a specific high integrability result. Our condition on the exponent $p(x)$ is more specific and weaker than the known co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.05559","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.05559/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":"2308.05559","created_at":"2026-07-05T06:40:02.350579+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.05559v1","created_at":"2026-07-05T06:40:02.350579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.05559","created_at":"2026-07-05T06:40:02.350579+00:00"},{"alias_kind":"pith_short_12","alias_value":"UKPATXQ5RJA4","created_at":"2026-07-05T06:40:02.350579+00:00"},{"alias_kind":"pith_short_16","alias_value":"UKPATXQ5RJA4R2WD","created_at":"2026-07-05T06:40:02.350579+00:00"},{"alias_kind":"pith_short_8","alias_value":"UKPATXQ5","created_at":"2026-07-05T06:40:02.350579+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/UKPATXQ5RJA4R2WD5CC7R45E6J","json":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J.json","graph_json":"https://pith.science/api/pith-number/UKPATXQ5RJA4R2WD5CC7R45E6J/graph.json","events_json":"https://pith.science/api/pith-number/UKPATXQ5RJA4R2WD5CC7R45E6J/events.json","paper":"https://pith.science/paper/UKPATXQ5"},"agent_actions":{"view_html":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J","download_json":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J.json","view_paper":"https://pith.science/paper/UKPATXQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.05559&json=true","fetch_graph":"https://pith.science/api/pith-number/UKPATXQ5RJA4R2WD5CC7R45E6J/graph.json","fetch_events":"https://pith.science/api/pith-number/UKPATXQ5RJA4R2WD5CC7R45E6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J/action/storage_attestation","attest_author":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J/action/author_attestation","sign_citation":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J/action/citation_signature","submit_replication":"https://pith.science/pith/UKPATXQ5RJA4R2WD5CC7R45E6J/action/replication_record"}},"created_at":"2026-07-05T06:40:02.350579+00:00","updated_at":"2026-07-05T06:40:02.350579+00:00"}