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For $p>2$, solutions may develop gradient singularities on the boundary in finite time, and examples of single-point gradient blowup on the boundary are known, but the space-profile in the tangential direction has remained a completely open problem. In the parameter range $2<p\\le 3$, for the case of a flat boundary and an isolated singularity at the origin, we give an answer to this question, obtaining"},"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":"1508.06766","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-27T09:21:16Z","cross_cats_sorted":[],"title_canon_sha256":"cc5c7b7af2214dfc747698be1cc9bf682d9116afaeb170f61c3910f696478d4c","abstract_canon_sha256":"cdda0871b93dda1f6c3780d0158c2e27e44d5d8e8c0ded096550fdafeb2e68bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:34.897666Z","signature_b64":"Dyjz3fdeGqxrQjMuI1njHcs+wYpaGbEqboyejcZCaWemHji3ifNQf7kGrKOBODz4FTpjzbAuryLKSqkGe110Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1d09c1f70c9df733dbcea60b26fc58320e9591aadf3852e3381aaeccea2d9cf","last_reissued_at":"2026-05-18T01:12:34.897279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:34.897279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The profile of boundary gradient blow-up for the diffusive Hamilton-Jacobi equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Porretta, Philippe Souplet","submitted_at":"2015-08-27T09:21:16Z","abstract_excerpt":"We consider the diffusive Hamilton-Jacobi equation $$u_t-\\Delta u=|\\nabla u|^p,$$ with Dirichlet boundary conditions in two space dimensions, which arises in the KPZ model of growing interfaces. 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