{"paper":{"title":"SBV regularity for Hamilton-Jacobi equations in $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camillo De Lellis, Roger Robyr, Stefano Bianchini","submitted_at":"2010-02-22T09:48:55Z","abstract_excerpt":"In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \\partial_t u + H(D_{x} u)=0 \\qquad \\textrm{in} \\Omega\\subset \\mathbb R\\times \\mathbb R^{n} . $$ In particular, under the assumption that the Hamiltonian $H\\in C^2(\\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\\partial_t u$ belong to the class $SBV_{loc}(\\Omega)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4087","kind":"arxiv","version":2},"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"}