{"paper":{"title":"Rigidity results for the capillary overdetermined problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Pieralberto Sicbaldi, Yuanyuan Lian","submitted_at":"2025-03-18T12:48:05Z","abstract_excerpt":"In this paper we obtain rigidity results for bounded positive solutions of the general capillary overdetermined problem \\begin{equation}\n  \\left\\{ \\begin{array} {ll} \\mathrm{div} \\left(\\frac{\\nabla u}{\\sqrt{1+|\\nabla u|^2}}\\right) + f(u) = 0 & \\mbox{in }\\; \\Omega,\\\\[1mm]\n  u= 0 & \\mbox{on }\\; \\partial \\Omega,\\\\[1mm] \\partial_{\\nu} u=\\kappa &\\mbox{on }\\; \\partial \\Omega, \\end{array}\\right. \\end{equation} where $f$ is a given $C^1$ function in $\\mathbb{R}$, $\\nu$ is the exterior unit normal, $\\kappa$ is a constant and $\\Omega \\subset \\mathbb{R}^n$ is a $C^1$ domain. Our main theorem states that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.14215","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.14215/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}