Neumann boundary value problem in domains of the Heisenberg Group ${\mathbb{H}}_n$

Abstract

Existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian on the Korányi ball of the Heisenberg group ${\mathbb{H}}_n$ are discussed. Explicit representations of Green's type function (Neumann function) for the half space and Korányi ball in ${\mathbb{H}}_n$ for circular functions have been obtained. These functions are then used on above regions in ${\mathbb{H}}_n$ to solve the inhomogeneous Neumann boundary value problem for circular data.