{"paper":{"title":"Solutions to overdetermined elliptic problems in nontrivial exterior domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Ros, David Ruiz, Pieralberto Sicbaldi","submitted_at":"2016-09-13T09:39:00Z","abstract_excerpt":"In this paper we construct nontrivial exterior domains $\\Omega \\subset \\mathbb{R}^N$, for all $N\\geq 2$, such that the problem $$\\left\\{ {ll} -\\Delta u +u -u^p=0,\\ u >0 & \\mbox{in }\\; \\Omega, {1mm]\n  \\ u= 0 & \\mbox{on }\\; \\partial \\Omega, [1mm]\n  \\ \\frac{\\partial u}{\\partial \\nu} = \\mbox{cte} & \\mbox{on }\\; \\partial \\Omega, \\right.$$ admits a positive bounded solution. This result gives a negative answer to the Berestycki-Caffarelli-Nirenberg conjecture on overdetermined elliptic problems in dimension 2, the only dimension in which the conjecture was still open. For higher dimensions, differen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03739","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"}