Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation

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 ∂ϕ∂z+∂∂t[ϕ2/2]=w, where w is a bounded measurable function.