Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups (Q961055)

The authors characterize the continuous distributional solutions of Burgers' equation in an open set in \(\mathbb{R}^2\) as those, which, considered as a graph in the Heisenberg group \(\mathbb{H}^1 = \mathbb{R}^3\) endowed with a left invariant metric \(d_\infty\) equivalent to the Carnot-Carathéodory metric, are intrinsic regular. The characterization is also extended to higher dimensional Heisenberg group \(\mathbb{H}^n = \mathbb{R}^{2n+1}\).