{"paper":{"title":"$C^{1,\\alpha}$-subelliptic regularity on SU(3) and compact, semi-simple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andr\\'as Domokos, Juan J. Manfredi","submitted_at":"2018-08-21T20:06:05Z","abstract_excerpt":"Let the vector fields $X_1, ... , X_{6}$ form an orthonormal basis of ${\\mathcal H}$, the orthogonal complement of a Cartan subalgebra (of dimension $2$) in SU(3). We prove that weak solutions $u$ to the degenerate subelliptic $p$-Laplacian $$ \\Delta_{\\mathcal{H},{p}} u(x)=\\sum_{i=1}^{6} X_i^{*}\\left(|\\nabla_{\\hspace{-0.1cm} {\\mathcal H}} u|^{p-2}X_{i}u \\right) =0,$$ have H\\\"older continuous horizontal derivatives $\\nabla_{\\hspace{-0.1cm}{\\mathcal H}} u=(X_1u, \\ldots, X_{6}u)$ for $p\\ge 2$. We also prove that a similar result holds for all compact connected semisimple Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07113","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"}