{"paper":{"title":"Transversally Lipschitz Harmonic Functions are Lipschitz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Sivaguru Ravisankar","submitted_at":"2012-03-21T02:48:28Z","abstract_excerpt":"Let \\Omega\\subset\\mathbb{R}^n be a bounded domain with C^\\infty boundary. We show that a harmonic function in \\Omega that is Lipschitz along a family of curves transversal to b\\Omega is Lipschitz in \\Omega. The space of Lipschitz functions we consider is defined using the notion of a majorant which is a certain generalization of the power functions t^\\alpha, 0<\\alpha<1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4641","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"}