Boundary regularity of the Neumann problem for the Kohn Laplacian on the Heisenberg group

This paper explores the regularity and existence theory for the Kohn Laplacian on a model class of domains in the Heisenberg group. A foliation of the Heisenberg group by spheres is exploited to expand the Kohn Laplacian via a partial Fourier decomposition. The main result is to establish sharp estimates even when the domains admit characteristic boundary points.