{"paper":{"title":"Serrin's overdetermined problem on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ignace Aristide Minlend, Mouhamed Moustapha Fall, Tobias Weth","submitted_at":"2016-12-12T14:47:32Z","abstract_excerpt":"We study Serrin's overdetermined boundary value problem \\begin{equation*}\n  -\\Delta_{S^N}\\, u=1 \\quad \\text{ in $\\Omega$},\\qquad u=0, \\; \\partial_\\eta u=\\textrm{const} \\quad \\text{on $\\partial \\Omega$} \\end{equation*} in subdomains $\\Omega$ of the round unit sphere $S^N \\subset \\mathbb{R}^{N+1}$, where $\\Delta_{S^N}$ denotes the Laplace-Beltrami operator on $S^N$. A subdomain $\\Omega$ of $S^N$ is called a Serrin domain if it admits a solution of this overdetermined problem. In our main result, we construct Serrin domains in $S^N$, $N \\ge 2$ which bifurcate from symmetric straight tubular neigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03717","kind":"arxiv","version":2},"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"}