Abstract
We give basic definitions and properties of the p-Laplace equation in the Heisenberg group. We establish existence and uniqueness results for the associated Dirichlet problem via variational methods and present some useful estimates. At the end we present the Hilbert–Haar existence theory for the variational functional associated to the p-Laplace equation which allows to prove that solutions to the non degenerate equation are Lipschitz continuous in domains satisfying a strict convexity condition.