{"paper":{"title":"Tug-of-War games and parabolic problems with spatial and time dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2012-08-30T17:37:57Z","abstract_excerpt":"In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form $$ {cases} K_{(x,t)}(D u)u_t (x,t)= \\frac12 <D^2 u J_{(x,t)}(D u),J_{(x,t)}(D u) (x,t)  &{in} \\Omega_T, u(x,t)=F(x)&{on}\\Gamma, {cases} $$ where $\\Omega_T=\\Omega\\times(0,T]$ and $\\Gamma$ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, $ u_t (x,t)= <D^2 u (x,t) \\frac{D u}{|Du|} (x,t),\\, \\frac{D u}{|Du|} (x,t)>$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6245","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"}