{"paper":{"title":"Rigidity results for elliptic boundary value problems: stable solutions for quasilinear equations with Neumann or Robin boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Pinamonti, Enrico Valdinoci, Serena Dipierro","submitted_at":"2017-09-22T20:16:39Z","abstract_excerpt":"We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions.\n  The method is based on a geometric formula of Poincar\\'e type, which is inspired by a classical work of Sternberg and Zumbrun and which gives an accurate description of the curvatures of the level sets of the stable solutions. {F}rom this, we show that the stable solutions of a quasilinear problem with Neumann data are necessarily constant.\n  As a byproduct of this, we obtain an alternative proof of a celebrated result of Casten and Holland, and Mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07934","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"}