On the $C^{1,\alpha}$ Regularity of $p$-Harmonic Functions in the   Heisenberg Group
  We present a proof of the local H\"older regularity of the horizontal derivatives of weak solutions to the $p$-Laplace equation in the Heisenberg group $\mathbb{H}^1$ for $p>4 $. 
Diego Ricciotti
math.AP