SECOND ORDER SOBOLEV REGULARITY FOR p-HARMONIC FUNCTIONS IN SU(3)

Let u be a weak solution to the degenerate subelliptic p-Laplacian equation Delta(H,p)u(x) = Sigma(6)(i=1) X-i(vertical bar del(H)u vertical bar(p-2) X(i)u) = 0, where H is the orthogonal complement of a Cartan subalgebra in SU(3) and its orthonormal basis is composed of the vector fields X-1 ..., X-6. We prove that when 1 < p < 7/2, the solution u has the second order horizontal Sobolev W(H,loc)(2,2)regularity.