{"paper":{"title":"Optimal regularity for the obstacle problem for the $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Henrik Shahgholian, John Andersson","submitted_at":"2014-02-20T10:42:21Z","abstract_excerpt":"In this paper we discuss the obstacle problem for the $p$-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising result we prove is the one for the $p$-obstacle problem: Find the smallest $u$ such that $$ \\hbox{div} (|\\nabla u|^{p-2}\\nabla u) \\leq 0, \\qquad u\\geq \\phi, \\qquad \\hbox{in } B_1, $$ with $\\phi \\in C^{1,1}(B_1)$ and given boundary datum on $\\partial B_1$. We prove that the solution is uniformly $C^{1,1}$ at free boundary points. Similar results are obtained i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4953","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"}