Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 27, pp. 1-15.

Title: Second order Sobolev regularity for p-harmonic functions in SU(3)
       
Author: Chengwei Yu (Beihang Univ., Haidian District, Beijing, China)

Abstract: 
Let u be a weak solution to the degenerate subelliptic p-Laplacian equation
$$
\Delta_{\mathcal{H},p}u(x)=\sum_{i=1}^6 X_i(|\nabla_{\mathcal{H}}u |^{p-2}X_iu)=0,
$$
where  $\mathcal{H}$ is the orthogonal complement of a Cartan subalgebra in SU(3) and its
orthonormal basis is composed of the vector fields X<sub>1</sub>,...,X<sub>6</sub>.
We prove that when  1&lt;p&lt;7/2, the solution u has the second order horizontal  Sobolev
$W^{2,2}_{\mathcal{H},\rm loc}$-regularity.

Submitted December 2, 2021. Published April 06, 2022.
Math Subject Classifications: 35H20, 35B65.
Key Words: p-Laplacian equation; SU(3); $W^{2,2}_{\mathcal{H},\rm loc}$-regularity; 
           Hessian matrix; p-harmonic function.