{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6SJCBU3QZC7H3GCVELYXCFY7QO","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":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665"},"schema_version":"1.0","source":{"id":"1109.4768","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4768v3","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"6SJCBU3QZC7H","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6SJCBU3QZC7H3GCV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6SJCBU3Q","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97","target":"graph","created_at":"2026-05-18T03:57:00Z","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":"This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\\\"older continuity estimates for solutions to $p$-degenerate elliptic equations in rough media with sources in the weak Lebesgue space $L_\\text{weak}^{\\frac{n}{p} + \\epsilon}$. For the borderline case, $f \\in L_\\text{weak}^{\\frac{n}{p}}$, solutions may not be bounded; nevertheless we show that solutions have bounded mean oscillation, in particular John-Nirenberg's exponential integrability estimates can be employed. All the resu","authors_text":"Eduardo V. Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title":"Sharp regularity for general Poisson equations with borderline sources"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4768","kind":"arxiv","version":3},"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":"sha256:4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b","target":"record","created_at":"2026-05-18T03:57:00Z","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":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665"},"schema_version":"1.0","source":{"id":"1109.4768","kind":"arxiv","version":3}},"canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","first_computed_at":"2026-05-18T03:57:00.391148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:00.391148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3HxtBsFA8L/kZBN0Odq2cnVh2uf5EvOwSvZ+C1Y2iGY40/EPOf9SiPZG3kFAzDnCYfmVzlkh+/LbwIZbWhZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:00.392014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4768","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b","sha256:f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97"],"state_sha256":"b4a77e02948d3bd861d9854d16ecadee2250fd6a1098615d19be2333a66af2a2"}