Generalizations of the Drift Laplace Equation in the Heisenberg Group and a Class of Grushin-Type Spaces

Abstract

We find fundamental solutions to p-Laplace equations with drift terms in the Heisenberg group and Grushin-type planes. These solutions are natural generalizations to the fundamental solutions discovered by Beals, Gaveau, and Greiner for the Laplace equation with drift term. Our results are independent of the results of Bieske and Childers, in that Bieske and Childers consider a generalization that focuses on a p-Laplace-type equation while we primarily concentrate on a generalization of the drift term.