{"paper":{"title":"Gradient bounds for p-harmonic systems with vanishing neumann data in a convex domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, John L. Lewis","submitted_at":"2013-05-01T03:27:41Z","abstract_excerpt":"Let $ \\ti \\Om $ be a bounded convex domain in Euclidean $ n $ space, $ \\hat x \\in \\ar \\ti \\Om, $ and $ r > 0. $ Let $ \\ti u = (\\ti u^1, \\ti u^2, \\dots, \\ti u^N) $ be a weak solution to \\[\\nabla \\cdot \\left (|\\nabla \\ti u |^{p-2} \\nabla \\ti u \\right) = 0 \\mbox{in} \\ti \\Om \\cap B (\\hat x, 4 r) \\mbox{with} |\\nabla \\ti u|^{p-2} \\, \\ti u_\\nu = 0 \\mbox{on} \\ar \\ti \\Om \\cap B (\\hat x, 4 r). \\] We show that sub solution type arguments for certain uniformly elliptic systems can be used to deduce that $ | \\nabla \\ti u | $ is bounded in $ \\ti \\Om \\cap B (\\hat x, r)$ with constants depending only on $ n, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0078","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"}