{"paper":{"title":"A stochastic differential game for the inhomogeneous $\\infty$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amarjit Budhiraja, Rami Atar","submitted_at":"2008-08-11T07:31:29Z","abstract_excerpt":"Given a bounded $\\mathcaligr{C}^2$ domain $G\\subset{\\mathbb{R}}^m$, functions $g\\in\\mathcaligr{C}(\\partial G,{\\mathbb{R}})$ and $h\\in\\mathcaligr {C}(\\bar{G},{\\mathbb{R}}\\setminus\\{0\\})$, let $u$ denote the unique viscosity solution to the equation $-2\\Delta_{\\infty}u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1457","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"}