{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:O7CLDW4RFJ4MPGWT2WMTQOPTPD","short_pith_number":"pith:O7CLDW4R","schema_version":"1.0","canonical_sha256":"77c4b1db912a78c79ad3d5993839f378c932a1bb05be88418b22b11967ea3a72","source":{"kind":"arxiv","id":"1802.09176","version":1},"attestation_state":"computed","paper":{"title":"Boundary higher integrability for very weak solutions of quasilinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karthik Adimurthi, Sun-Sig Byun","submitted_at":"2018-02-26T06:19:46Z","abstract_excerpt":"We prove boundary higher integrability for the (spatial) gradient of \\emph{very weak} solutions of quasilinear parabolic equations of the form $$u_t - \\text{div}\\,\\mathcal{A}(x,t, \\nabla u)=0 \\quad \\text{on} \\ \\Omega \\times \\mathbb{R},$$ where the non-linear structure $\\text{div}\\,\\mathcal{A}(x, t,\\nabla u)$ is modelled after the $p$-Laplace operator. To this end, we prove that the gradients satisfy a reverse H\\\"older inequality near the boundary. In order to do this, we construct a suitable test function which is Lipschitz continuous and preserves the boundary values. \\emph{These results are "},"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":"1802.09176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-26T06:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"9ea4b6ebab07ad6be1d7d656cc1f83fff8721b202a96abfd86e256d1b3d79ac2","abstract_canon_sha256":"fe059856947df0ea174937752cdd6c6fd0a3eab68c6f061a31d220d22ccbda59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:34.492969Z","signature_b64":"drIecOoBRZtin28mxvRmvQYaa4K2wpogmJdtx2SIP2iy2nFtY7L20X3Y+cDneIZaf68x9h2h8/O7KR01dhQhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77c4b1db912a78c79ad3d5993839f378c932a1bb05be88418b22b11967ea3a72","last_reissued_at":"2026-05-18T00:22:34.492269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:34.492269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary higher integrability for very weak solutions of quasilinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karthik Adimurthi, Sun-Sig Byun","submitted_at":"2018-02-26T06:19:46Z","abstract_excerpt":"We prove boundary higher integrability for the (spatial) gradient of \\emph{very weak} solutions of quasilinear parabolic equations of the form $$u_t - \\text{div}\\,\\mathcal{A}(x,t, \\nabla u)=0 \\quad \\text{on} \\ \\Omega \\times \\mathbb{R},$$ where the non-linear structure $\\text{div}\\,\\mathcal{A}(x, t,\\nabla u)$ is modelled after the $p$-Laplace operator. To this end, we prove that the gradients satisfy a reverse H\\\"older inequality near the boundary. In order to do this, we construct a suitable test function which is Lipschitz continuous and preserves the boundary values. \\emph{These results are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09176","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":"1802.09176","created_at":"2026-05-18T00:22:34.492399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.09176v1","created_at":"2026-05-18T00:22:34.492399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09176","created_at":"2026-05-18T00:22:34.492399+00:00"},{"alias_kind":"pith_short_12","alias_value":"O7CLDW4RFJ4M","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"O7CLDW4RFJ4MPGWT","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"O7CLDW4R","created_at":"2026-05-18T12:32:43.782077+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/O7CLDW4RFJ4MPGWT2WMTQOPTPD","json":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD.json","graph_json":"https://pith.science/api/pith-number/O7CLDW4RFJ4MPGWT2WMTQOPTPD/graph.json","events_json":"https://pith.science/api/pith-number/O7CLDW4RFJ4MPGWT2WMTQOPTPD/events.json","paper":"https://pith.science/paper/O7CLDW4R"},"agent_actions":{"view_html":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD","download_json":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD.json","view_paper":"https://pith.science/paper/O7CLDW4R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.09176&json=true","fetch_graph":"https://pith.science/api/pith-number/O7CLDW4RFJ4MPGWT2WMTQOPTPD/graph.json","fetch_events":"https://pith.science/api/pith-number/O7CLDW4RFJ4MPGWT2WMTQOPTPD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD/action/storage_attestation","attest_author":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD/action/author_attestation","sign_citation":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD/action/citation_signature","submit_replication":"https://pith.science/pith/O7CLDW4RFJ4MPGWT2WMTQOPTPD/action/replication_record"}},"created_at":"2026-05-18T00:22:34.492399+00:00","updated_at":"2026-05-18T00:22:34.492399+00:00"}