{"paper":{"title":"Symmetry for a general class of overdetermined elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Friedemann Brock","submitted_at":"2015-12-16T10:50:45Z","abstract_excerpt":"Let $\\Omega $ be a bounded domain in $\\mathbb{R} ^N $, and let $u\\in C^1 (\\overline{\\Omega }) $ be a weak solution of the following overdetermined BVP: $-\\nabla (g(|\\nabla u|)|\\nabla u|^{-1} \\nabla u )=f(|x|,u)$, $ u>0 $ in $\\Omega $ and $u(x)=0, \\ |\\nabla u (x)| =\\lambda (|x|)$ on $\\partial \\Omega $, where $g\\in C([0,+\\infty ))\\cap C^1 ((0,+\\infty ) ) $ with $g(0)=0$, $g'(t)>0$ for $t>0$, $f\\in C([0,+\\infty )) \\times [0, +\\infty ) )$, $f$ is nonincreasing in $|x|$, $\\lambda \\in C([0, +\\infty )) $ and $\\lambda $ is positive and nondecreasing. We show that $\\Omega $ is a ball and $u$ satisfies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05126","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"}