{"paper":{"title":"A maximum principle on unbounded domains and a Liouville theorem for fractional p-harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leyun Wu, Wenxiong Chen","submitted_at":"2019-05-24T01:07:16Z","abstract_excerpt":"In this paper, we establish the following Liouville theorem for fractional \\emph{p}-harmonic functions.\n  {\\em Assume that $u$ is a bounded solution of $$(-\\lap)^s_p u(x) = 0, \\;\\; x \\in \\mathbb{R}^n,$$ with $0<s<1$ and $p \\geq 2$.\n  Then $u$ must be constant.}\n  A new idea is employed to prove this result, which is completely different from the previous ones in deriving Liouville theorems.\n  For any given hyper-plane in $\\mathbb{R}^n$, we show that $u$ is symmetric about the plane. To this end, we established a {\\em maximum principle} for anti-symmetric functions on any half space. We believe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09986","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"}