{"paper":{"title":"A note on 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","submitted_at":"2014-01-17T15:31:14Z","abstract_excerpt":"We consider the solution of the torsion problem $-\\Delta u=1$ in $\\Omega$ and $u=0$ on $\\partial \\Omega$. Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\\nu$ is constant on $\\partial \\Omega$, then $\\Omega$ must be a ball. In a recent paper, it has been conjectured that Serrin's theorem may be obtained {\\it by stability} in the following way: first, for the solution $u$ of the torsion problem prove the estimate $$ r_e-r_i\\leq C_t\\,\\Bigl(\\max_{\\Gamma_t} u-\\min_{\\Gamma_t} u\\Bigr) $$ for some constant $C_t$ depending on $t$, where $r_e$ and $r_i$ are the radii of an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4385","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"}