{"paper":{"title":"Stochastic approach for a multivalued Dirichlet-Neumann problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Aurel Rascanu, Lucian Maticiuc","submitted_at":"2008-08-06T11:38:40Z","abstract_excerpt":"We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality with a nonlinear multivalued Neumann-Dirichlet boundary condition:% {equation*} \\{{array}{r} \\dfrac{\\partial u(t,x)}{\\partial t}-\\mathcal{L}_{t}u(t,x) {+}{% \\partial \\phi}\\big(u(t,x)\\big)\\ni f\\big(t,x,u(t,x),(\\nabla u\\sigma)(t,x)\\big), t>0, x\\in \\mathcal{D},\\medskip \\multicolumn{1}{l}{\\dfrac{\\partial u(t,x)}{\\partial n}+{\\partial \\psi}\\big(% u(t,x)\\big)\\ni g\\big(t,x,u(t,x)\\big), t>0, x\\in Bd(\\mathcal{D}%),\\multicolumn{1}{l}{u(0,x)=h(x), x\\in \\bar{\\mathcal{D}},}% {array}%. {equation*}% where $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0817","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"}