{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W53NEMXYDJZ4RUIULL62FSEGK7","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":"f148a2e06c09fc6c75ef390369109f55c2467014775c9c7f9109579822638c7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-08T13:56:12Z","title_canon_sha256":"11233b5e2099462cb6bb9ec98c3f3acb1404600c487dd58082ae2fe4351816fd"},"schema_version":"1.0","source":{"id":"1902.03080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03080","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03080v1","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03080","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"W53NEMXYDJZ4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"W53NEMXYDJZ4RUIU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"W53NEMXY","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:31248accf97907efe145db5aab8873aeb7d88ef33274d3763211b973611364c8","target":"graph","created_at":"2026-05-17T23:54:28Z","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 consider the diffusive Hamilton-Jacobi equation $u_t - \\Delta u = |\\nabla u|^p$ in a bounded planar domain with zero Dirichlet boundary condition. It is known that, for $p>2$, the solutions to this problem can exhibit gradient blow-up (GBU) at the boundary. In this paper we study the possibility of the GBU set being reduced to a single point. In a previous work [Y.-X. Li, Ph. Souplet, 2009], it was shown that single point GBU solutions can be constructed in very particular domains, i.e.~locally flat domains and disks. Here, we prove the existence of single point GBU solutions in a large cla","authors_text":"Carlos Esteve","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-08T13:56:12Z","title":"Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03080","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:ac230912197e2c9883c5b04b50a35d8f0ace2a4b8a009c8aa8c4572e5cd73eb0","target":"record","created_at":"2026-05-17T23:54:28Z","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":"f148a2e06c09fc6c75ef390369109f55c2467014775c9c7f9109579822638c7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-08T13:56:12Z","title_canon_sha256":"11233b5e2099462cb6bb9ec98c3f3acb1404600c487dd58082ae2fe4351816fd"},"schema_version":"1.0","source":{"id":"1902.03080","kind":"arxiv","version":1}},"canonical_sha256":"b776d232f81a73c8d1145afda2c88657e243a43ffcea22a8eefe280a044bbccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b776d232f81a73c8d1145afda2c88657e243a43ffcea22a8eefe280a044bbccf","first_computed_at":"2026-05-17T23:54:28.020214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:28.020214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3GeGXLN8TwYPiCJds56O1PBGbW4TPkXimv9ZwxjcNb5T5I9ALrPoeAUoIS6SOGVPcqpiWL/WSxRsuj617JtCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:28.020937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac230912197e2c9883c5b04b50a35d8f0ace2a4b8a009c8aa8c4572e5cd73eb0","sha256:31248accf97907efe145db5aab8873aeb7d88ef33274d3763211b973611364c8"],"state_sha256":"f381dd892aef4bb9a386d7b2b5829f536c436d9b7d454761812daaa957f7d383"}