{"paper":{"title":"A general class of free boundary problems for fully nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Figalli, H. Shahgholian","submitted_at":"2012-12-23T16:08:33Z","abstract_excerpt":"In this paper we study the fully nonlinear free boundary problem $$ {{array}{ll} F(D^2u)=1 & \\text{a.e. in}B_1 \\cap \\Omega |D^2 u| \\leq K & \\text{a.e. in}B_1\\setminus\\Omega, {array}. $$ where $K>0$, and $\\Omega$ is an unknown open set.\n  Our main result is the optimal regularity for solutions to this problem: namely, we prove that $W^{2,n}$ solutions are locally $C^{1,1}$ inside $B_1$. Under the extra condition that $\\Omega \\supset \\{D u\\neq 0 \\}$, and a uniform thickness assumption on the coincidence set $\\{D u = 0 \\}$, we also show local regularity for the free boundary $\\partial\\Omega\\cap B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5809","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"}