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

Abstract

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 $\frac{\partial \varphi }{\partial z}+\frac{\partial }{\partial t}[{\varphi }^2/2]=w$, where w is a bounded measurable function.