{"paper":{"title":"A limiting free boundary problem with gradient constraint and Tug-of-War games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao V\\'itor da Silva, Julio D. Rossi, Pablo Blanc","submitted_at":"2017-12-18T21:26:50Z","abstract_excerpt":"In this manuscript we deal with regularity issues and the asymptotic behaviour (as $p \\to \\infty$) of solutions for elliptic free boundary problems of $p-$Laplacian type ($2 \\leq p< \\infty$): \\begin{equation*} -\\Delta_p u(x) + \\lambda_0(x)\\chi_{\\{u>0\\}}(x) = 0 \\quad \\mbox{in} \\quad \\Omega \\subset \\mathbb{R}^N, \\end{equation*} with a prescribed Dirichlet boundary data, where $\\lambda_0>0$ is a bounded function and $\\Omega$ is a regular domain. First, we prove the convergence as $p\\to \\infty$ of any family of solutions $(u_p)_{p\\geq 2}$, as well as we obtain the corresponding limit operator (in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06683","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"}