Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions   of a balance equation
  In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation \phi_y+ [\phi^{2}/2]_t=w, where w is a bounded function depending on \phi. 
Francesco Bigolin, Laura Caravenna, Francesco Serra Cassano
math.DG math.AP