{"paper":{"title":"Symmetry and linear stability in Serrin's overdetermined problem via the stability of the parallel surface problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo, Rolando Magnanini, Vincenzo Vespri","submitted_at":"2015-01-29T18:17:58Z","abstract_excerpt":"We consider the solution of the problem $$ -\\Delta u=f(u) \\ \\mbox{ and } \\ u>0 \\ \\ \\mbox{ in } \\ \\Omega, \\ \\ u=0 \\ \\mbox{ on } \\ \\Gamma, $$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^N$ with boundary $\\Gamma$ of class $C^{2,\\tau}$, $0<\\tau<1$, and $f$ is a locally Lipschitz continuous non-linearity. Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\\nu$ is constant on $\\Gamma$, then $\\Omega$ must be a ball.\n  In [CMS2], it has been conjectured that Serrin's theorem may be obtained by stability in the following way: first, for a solution $u$ prove the estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07531","kind":"arxiv","version":3},"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"}