The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ n $\mathbb H_{n}$

Abstract

The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Koranyi ball on the Heisenberg group \(\mathbb {H}_{n}\) are discussed. Explicit representation for a Green’s type function (Neumann function) for the Koranyi ball in \(\mathbb {H}_{n}\) for circular functions has been obtained. This function is then used on the above region in \(\mathbb {H}_{n}\) to solve the inhomogeneous Neumann boundary value problem for certain circular data.