{"paper":{"title":"Gradient flows with jumps associated with nonlinear Hamilton-Jacobi equations with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Constantin Varsan, Saima Parveen","submitted_at":"2012-03-08T10:38:31Z","abstract_excerpt":"We analyze gradient flows with jumps generated by a finite set of complete vector fields in involution using some Radon measures $u\\in \\mathcal{U}_a$ as admissible perturbations. Both the evolution of a bounded gradient flow $\\{x^u(t,\\l)\\in B(x^*,3\\g)\\subseteq \\mbn: \\,t\\in[0,T],\\,\\l\\in B(x^*,2\\g)\\}$ and the unique solution $\\l=\\psi^u(t,x)\\in B(x^*,2\\g)\\subseteq \\mbn$ of integral equation $x^u(t,\\l)=x\\in B(x^*,\\g), \\,t\\in[0,T]$, are described using the corresponding gradient representation associated with flow and Hamilton-jacobi equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1741","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"}