{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:W53NEMXYDJZ4RUIULL62FSEGK7","short_pith_number":"pith:W53NEMXY","schema_version":"1.0","canonical_sha256":"b776d232f81a73c8d1145afda2c88657e243a43ffcea22a8eefe280a044bbccf","source":{"kind":"arxiv","id":"1902.03080","version":1},"attestation_state":"computed","paper":{"title":"Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Esteve","submitted_at":"2019-02-08T13:56:12Z","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"},"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":"1902.03080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-08T13:56:12Z","cross_cats_sorted":[],"title_canon_sha256":"11233b5e2099462cb6bb9ec98c3f3acb1404600c487dd58082ae2fe4351816fd","abstract_canon_sha256":"f148a2e06c09fc6c75ef390369109f55c2467014775c9c7f9109579822638c7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:28.020937Z","signature_b64":"G3GeGXLN8TwYPiCJds56O1PBGbW4TPkXimv9ZwxjcNb5T5I9ALrPoeAUoIS6SOGVPcqpiWL/WSxRsuj617JtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b776d232f81a73c8d1145afda2c88657e243a43ffcea22a8eefe280a044bbccf","last_reissued_at":"2026-05-17T23:54:28.020214Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:28.020214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Esteve","submitted_at":"2019-02-08T13:56:12Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03080","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":"1902.03080","created_at":"2026-05-17T23:54:28.020335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03080v1","created_at":"2026-05-17T23:54:28.020335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03080","created_at":"2026-05-17T23:54:28.020335+00:00"},{"alias_kind":"pith_short_12","alias_value":"W53NEMXYDJZ4","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"W53NEMXYDJZ4RUIU","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"W53NEMXY","created_at":"2026-05-18T12:33:30.264802+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/W53NEMXYDJZ4RUIULL62FSEGK7","json":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7.json","graph_json":"https://pith.science/api/pith-number/W53NEMXYDJZ4RUIULL62FSEGK7/graph.json","events_json":"https://pith.science/api/pith-number/W53NEMXYDJZ4RUIULL62FSEGK7/events.json","paper":"https://pith.science/paper/W53NEMXY"},"agent_actions":{"view_html":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7","download_json":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7.json","view_paper":"https://pith.science/paper/W53NEMXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03080&json=true","fetch_graph":"https://pith.science/api/pith-number/W53NEMXYDJZ4RUIULL62FSEGK7/graph.json","fetch_events":"https://pith.science/api/pith-number/W53NEMXYDJZ4RUIULL62FSEGK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7/action/storage_attestation","attest_author":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7/action/author_attestation","sign_citation":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7/action/citation_signature","submit_replication":"https://pith.science/pith/W53NEMXYDJZ4RUIULL62FSEGK7/action/replication_record"}},"created_at":"2026-05-17T23:54:28.020335+00:00","updated_at":"2026-05-17T23:54:28.020335+00:00"}