{"paper":{"title":"Maximal solutions for the Infinity-eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort, Joao V. da Silva, Julio D. Rossi","submitted_at":"2017-04-06T15:00:34Z","abstract_excerpt":"In this article we prove that the first eigenvalue of the $\\infty-$Laplacian $$ \\left\\{ \\begin{array}{rclcl}\n  \\min\\{ -\\Delta_\\infty v,\\, |\\nabla v|-\\lambda_{1, \\infty}(\\Omega) v \\} & = & 0 & \\text{in} & \\Omega v & = & 0 & \\text{on} & \\partial \\Omega, \\end{array} \\right. $$ has a unique (up to scalar multiplication) maximal solution. This maximal solution can be obtained as the limit as $\\ell \\nearrow 1$ of concave problems of the form $$ \\left\\{ \\begin{array}{rclcl}\n  \\min\\{ -\\Delta_\\infty v_{\\ell},\\, |\\nabla v_{\\ell}|-\\lambda_{1, \\infty}(\\Omega) v_{\\ell}^{\\ell} \\} & = & 0 & \\text{in} & \\Omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01875","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"}