{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QEAZHPJQZLRAQTT7RZV6V7GIHQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1097323a444f229c94acfc3fcecc7ee738be27ce5d9cda079865a6054a6cf215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-04T04:03:44Z","title_canon_sha256":"0dde4a40ccecebed78e8898b6ead6716e16d647e1622ed2f10d1154dd94183a9"},"schema_version":"1.0","source":{"id":"1806.00944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00944","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00944v1","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00944","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"QEAZHPJQZLRA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QEAZHPJQZLRAQTT7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QEAZHPJQ","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:bdd9f434e394f4b6ed83275421d734ce79e165a26d79915034ae1d73177b5611","target":"graph","created_at":"2026-05-18T00:14:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study quasilinear parabolic equations with the nonlinearity structure modeled after the $p(x,t)$-Laplacian on nonsmooth domains. The main goal is to obtain end point Calder\\'on-Zygmund type estimates in the variable exponent setting. In a recent work \\cite{byun2016nonlinear}, the estimates obtained were strictly above the natural exponent $p(x,t)$ and hence there was a gap between the natural energy estimates and the estimates above $p(x,t)$ (see \\eqref{energy} and \\eqref{byunok}). Here, we bridge this gap to obtain the end point case of the estimates obtained in \\cite{byun20","authors_text":"Jung-Tae Park, Karthik Adimurthi, Sun-Sig Byun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-04T04:03:44Z","title":"End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00944","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:291fdd52191abfdca2bab2fb8c2f71979cff3aaf2c2b80878b36720462f4143a","target":"record","created_at":"2026-05-18T00:14:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1097323a444f229c94acfc3fcecc7ee738be27ce5d9cda079865a6054a6cf215","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-04T04:03:44Z","title_canon_sha256":"0dde4a40ccecebed78e8898b6ead6716e16d647e1622ed2f10d1154dd94183a9"},"schema_version":"1.0","source":{"id":"1806.00944","kind":"arxiv","version":1}},"canonical_sha256":"810193bd30cae2084e7f8e6beafcc83c2149be18a81c2c823fa0ac9858d7768d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"810193bd30cae2084e7f8e6beafcc83c2149be18a81c2c823fa0ac9858d7768d","first_computed_at":"2026-05-18T00:14:17.924202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:17.924202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FzwPoBuEg+RYVREBuV/meGSjXuK9M8G9bEbDU6H7Gtq6zNA2ZLP7hzfgq2vpHW+uSessLVuBzZqMhbGP3RkmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:17.925013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:291fdd52191abfdca2bab2fb8c2f71979cff3aaf2c2b80878b36720462f4143a","sha256:bdd9f434e394f4b6ed83275421d734ce79e165a26d79915034ae1d73177b5611"],"state_sha256":"4ea2e2596ec59bea0f5ced9902f851af5dc24958c443052c60b3d8c7fb410aae"}