{"paper":{"title":"The Singular Set of Higher Dimensional Unstable Obstacle Type Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georg Weiss, Henrik Shahgholian, John Andersson","submitted_at":"2012-07-14T07:00:13Z","abstract_excerpt":"In this paper we will investigate the singular points of the following unstable free boundary problem: {equation}\\label{Eq} \\Delta u= -\\chi_{\\{u>0\\}} \\quad\\quad\\textrm{in} B_1(0) {equation} where $\\chi_{\\{u>0\\}}$ is the characteristic function of the set $\\{u>0\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3398","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"}