Regularity of subelliptic p-harmonic systems with subcritical growth in Carnot group

For a class of subelliptic p  -harmonic systems with the subcritical growth defined in Carnot groups, we prove that the weak solutions belong to Γloc1,α-regularity with respect to the Carnot–Caratheodory distance provided that p is close to 2. As a consequence, we make it clear that the critical growth of nonlinearity for p-harmonic type systems in Carnot groups is just a sharp borderline of partial regularity of the small “excess” energy due to the counterexamples of p-harmonic maps with p close to 2.