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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.07113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-21T20:06:05Z","cross_cats_sorted":[],"title_canon_sha256":"98853233963ac7eae99b1c5cb9a62c370d19cf992592c5cd23339af4720b1421","abstract_canon_sha256":"ff7d237a508941d1c0298f3d40a57bbed26d33702ff1fff9ee3a93595baf9469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:34.853919Z","signature_b64":"SZfS93QoLQA4h5AhkhzGn90RpHmgTrYxw5NRCZG8Vgb7x9S9shvi5MCEAhsUDx0xojiWsY2HsvRaZsmuOfwgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f6f01a0fe087df585d7a24d27c5833a6ef04b48935e6e6aefb4bbba691436e4","last_reissued_at":"2026-05-18T00:00:34.853433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:34.853433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $p\\ge 2$. 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