{"paper":{"title":"Radial symmetry for p-harmonic functions in exterior and punctured domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giorgio Poggesi","submitted_at":"2018-01-22T14:03:00Z","abstract_excerpt":"We prove symmetry for the p-capacitary potential satisfying $$ \\Delta_p u = 0 \\, \\mbox{ in } \\mathbb{R}^N \\setminus \\overline{\\Omega} , \\; u=1 \\, \\mbox{ on } \\Gamma, \\; \\lim_{|x|\\rightarrow \\infty} u(x)=0 , \\; \\; \\; \\; \\; \\; \\; \\; 1<p<N, $$ under Serrin's overdetermined condition $$ | \\nabla u| = c \\mbox{ on } \\Gamma. $$ Here $\\Omega$ is any bounded domain on which no a priori assumption is made, and $\\Gamma$ denotes its boundary. Our result improves on a work of Garofalo and Sartori, where the same conclusion was obtained when $\\Omega$ is star-shaped. Our proof uses the maximum principle for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07105","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"}