$C^{1,α}$-Regularity for $p$-Harmonic Functions in SU(3)

Abstract

This artical concerns the $C^{1,α}_{ {\rm loc}}$-regularity of weak solutions $u$ to the degenerate subelliptic $p$-Laplacian equation $$\Delta_{\mathcal{H},p}u(x)=\sum\limits_{i=1}^6X_i^*(|\nabla_{\mathcal{H}}u|^{p-2}X_iu)=0,$$where $\mathcal{H}$ is the orthogonal complement of a Cartan subalgebra in SU(3) with the orthonormal basis composed of the vector fields $X_1,...,X_6.$ When $1