{"paper":{"title":"Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Minne, Emanuel Indrei","submitted_at":"2014-03-17T23:00:40Z","abstract_excerpt":"We consider fully nonlinear obstacle-type problems of the form \\begin{equation*} \\begin{cases} F(D^{2}u,x)=f(x) & \\text{a.e. in}B_{1}\\cap\\Omega,|D^{2}u|\\le K & \\text{a.e. in}B_{1}\\backslash\\Omega, \\end{cases} \\end{equation*} where $\\Omega$ is an unknown open set and $K>0$. In particular, structural conditions on $F$ are presented which ensure that $W^{2,n}(B_1)$ solutions achieve the optimal $C^{1,1}(B_{1/2})$ regularity when $f$ is H\\\"older continuous. Moreover, if $f$ is positive on $\\overline B_1$, Lipschitz continuous, and $\\{u\\neq 0\\} \\subset \\Omega$, then we obtain local $C^1$ regularity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4300","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"}