{"paper":{"title":"H\\\"older stability for Serrin's overdetermined 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":"2014-10-28T20:24:32Z","abstract_excerpt":"In a bounded domain $\\Omega$, we consider a positive solution of the problem $\\Delta u+f(u)=0$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $f:\\mathbb{R}\\to\\mathbb{R}$ is a locally Lipschitz continuous function. Under sufficient conditions on $\\Omega$ (for instance, if $\\Omega$ is convex), we show that $\\partial\\Omega$ is contained in a spherical annulus of radii $r_i<r_e$, where $r_e-r_i\\leq C\\,[u_\\nu]_{\\partial\\Omega}^\\alpha$ for some constants $C>0$ and $\\alpha\\in (0,1]$. Here, $[u_\\nu]_{\\partial\\Omega}$ is the Lipschitz seminorm on $\\partial\\Omega$ of the normal derivative of $u$. This re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7791","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"}