A Neumann type problem on an unbounded domain in the Heisenberg group

TL;DR

This paper investigates the well-posedness of the Neumann problem for the Kohn-Laplacian on unbounded domains in the Heisenberg group, constructing the Neumann function and providing explicit solutions.

Contribution

It introduces a new analysis of the Neumann problem in the Heisenberg group, including explicit construction of the Neumann function and solution representation.

Findings

Established well-posedness of the Neumann problem

Constructed explicit Neumann function

Provided explicit solution formulas

Abstract

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.