{"paper":{"title":"Almost Everywhere Regularity for the Free Boundary of the Normalized p-harmonic Obstacle problem $p>2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John Andersson","submitted_at":"2016-11-14T14:47:10Z","abstract_excerpt":"Let $u$ be a solution to the normalized p-harmonic obstacle problem with $p>2$. That is, $u\\in W^{1,p}(B_1(0))$, $2<p<\\infty$, $u\\ge 0$ and $$ \\d\\left( |\\nabla u|^{p-2}\\nabla u\\right)=\\chi_{\\{u>0\\}}\\textrm{ in }B_1(0) $$ where $u(x)\\ge 0$ and $\\chi_A$ is the characteristic function of the set $A$. Our main result is that for almost every free boundary point, with respect to the $(n-1)-$Hausdorff measure, there is a neighborhood where the free boundary is a $C^{1,\\beta}-$graph. That is, for $\\H^{n-1}-$a.e. point $x^0\\in \\partial \\{u>0\\}\\cap B_1(0)$ there is an $r>0$ such that $B_r(x^0)\\cap \\par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04397","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"}