(P,Q)-SUB-LAPLACIANS ON THE HEISENBERG GROUP

Abstract

The main purpose of this capstone project is to do some analysis related to (p,q)-sub-Laplacians on the Heisenberg group. In the first part of the project, Green’s identities for (p,q)-sub-Laplacians are given on the Heisenberg group and used further in proof of the uniqueness of a weak solution of a nonlinear Dirichlet boundary value problem for the (p,q)-sub-Laplacian. Moreover, concepts of CC and Kaplan balls are discussed to illustrate the smoothness of the considered domain for the BVP.