Geodesic
On the Regularity of p-Harmonic Functions in the Heisenberg Group
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 243-253

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We describe some recent results obtained in [29], where we prove regularity theorems for sub-elliptic equations in (horizontal) divergence form defined in the Heisenberg group, and exhibiting polynomial growth of order p. The main result tells that when $p \in [2,4)$ solutions to possibly degenerate equations are locally Lipschitz continuous with respect to the intrinsic distance. In particular, such result applies to p-harmonic functions in the Heisenberg group. Explicit estimates are obtained, and eventually applied to obtain the suitable Calderón-Zygmund theory for the associated non-homogeneous problems. 
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Mingione, Giuseppe; Anna, Zatorska-Goldstein; Zhong, Xiao. On the Regularity of p-Harmonic Functions in the Heisenberg Group. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 243-253. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a9/