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 Kor\'anyi ball of the Heisenberg group $\mathbb{H}_n$ are discussed. Explicit representations of Green's type function (Neumann function) for the half space and Kor\'anyi 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.