Distributional solutions of Burgersʹ equation and intrinsic regular graphs in Heisenberg groups

In the present paper we will characterize the continuous distributional solutions of Burgersʹ equation as those which induce intrinsic regular graphs in the first Heisenberg group H 1 ≡ R 3 , endowed with a left-invariant metric d ∞ equivalent to its Carnot–Carathéodory metric. We will also extend the characterization to higher Heisenberg groups H n ≡ R 2 n + 1 .