{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D4RYOQ74BXEKDM2R37PM3WEBWS","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":"af0ed8fe990fe86acac9b79972322691fc8294237ff2e5e6e3ce7247c73052a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-30T02:43:25Z","title_canon_sha256":"09276da23b29dd2f9f672e95c0c6b95b0f486bc66420bf0cdf0fda3a03bd25d2"},"schema_version":"1.0","source":{"id":"1810.12496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12496","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12496v1","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12496","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"D4RYOQ74BXEK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4RYOQ74BXEKDM2R","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4RYOQ74","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:c75341ab82c23d029486c8511f3aeaf54bbb3df97d0521a2c1303848d9c4669d","target":"graph","created_at":"2026-05-18T00:01:56Z","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":"We study regularity for solutions of quasilinear elliptic equations of the form $\\div \\A(x,u,\\nabla u) = \\div \\F $ in bounded domains in $\\R^n$. The vector field $\\A$ is assumed to be continuous in $u$, and its growth in $\\nabla u$ is like that of the $p$-Laplace operator. We establish interior gradient estimates in weighted Morrey spaces for weak solutions $u$ to the equation under a small BMO condition in $x$ for $\\A$. As a consequence, we obtain that $\\nabla u$ is in the classical Morrey space $\\calM^{q,\\lambda}$ or weighted space $L^q_w$ whenever $|\\F|^{\\frac{1}{p-1}}$ is respectively in $","authors_text":"Giuseppe Di Fazio, Truyen Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-30T02:43:25Z","title":"Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12496","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":"sha256:6c16535670ef47a85d17842bba7108f946515c119a64b1856372d8fb05ae0a49","target":"record","created_at":"2026-05-18T00:01:56Z","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":"af0ed8fe990fe86acac9b79972322691fc8294237ff2e5e6e3ce7247c73052a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-30T02:43:25Z","title_canon_sha256":"09276da23b29dd2f9f672e95c0c6b95b0f486bc66420bf0cdf0fda3a03bd25d2"},"schema_version":"1.0","source":{"id":"1810.12496","kind":"arxiv","version":1}},"canonical_sha256":"1f238743fc0dc8a1b351dfdecdd881b4a430985a2ad4e84dee843e9ac0e518ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f238743fc0dc8a1b351dfdecdd881b4a430985a2ad4e84dee843e9ac0e518ea","first_computed_at":"2026-05-18T00:01:56.935019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:56.935019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJhWXcaaEGqF8FqDtwfFvo0nrsPNepv1+q9G7iUKTQ/ojV6gloFalAMcMsVUje8Hdg/EAr71gw78ZjASbSa1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:56.935632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c16535670ef47a85d17842bba7108f946515c119a64b1856372d8fb05ae0a49","sha256:c75341ab82c23d029486c8511f3aeaf54bbb3df97d0521a2c1303848d9c4669d"],"state_sha256":"b9f02351401334feb286dd0c9e162a038975e64b9ea96d45fea5e02dccccc435"}