{"paper":{"title":"Layered Viscosity Solutions of Nonautonomous Hamilton-Jacobi Equations: Semiconvexity and Relations to Characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nguyen Hoang, Nguyen Mau Nam","submitted_at":"2012-04-25T12:01:24Z","abstract_excerpt":"We construct an explicit representation of viscosity solutions of the Cauchy problem for the Hamilton-Jacobi equation $(H,\\sigma)$ on a given domain $\\Omega= (0,T)\\times \\R^n.$ It is known that, if the Hamiltonian $H = H(t,p)$ is not a convex (or concave) function in $p$, or $H(\\cdot, p)$ may change its sign on $(0,T)$, then the Hopf-type formula does not define a viscosity solution on $\\Omega.$ Under some assumptions for $H(t,p)$ on the subdomains $(t_i, t_{i+1})\\times \\R^n\\subset \\Omega$, we are able to arrange \"partial solutions\" given by the Hopf-type formula to get a viscosity solution on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5628","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"}