{"paper":{"title":"A rigidity result for overdetermined elliptic problems in the plane","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":"2015-05-21T12:57:39Z","abstract_excerpt":"Let $f:[0,+\\infty) \\to \\mathbb{R}$ be a (locally) Lipschitz function and $\\Omega \\subset \\mathbb{R}^2$ a $C^{1,\\alpha}$ domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined elliptic problem $$ \\left\\{\\begin{array} {ll} \\Delta u + f(u) = 0 & \\mbox{in }\\; \\Omega\n  \\\\ u= 0\\, \\, \\, , \\, \\, \\, \\frac{\\partial u}{\\partial \\vec{\\nu}}=1 &\\mbox{on }\\; \\partial \\Omega \\end{array}\\right. $$ we prove that $\\Omega$ is a half-plane. In particular, we obtain a partial answer to a question raised by H. Berestycki, L. Caffarelli and L. Nirenberg in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05707","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"}