Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 99, pp. 1-13.

Title: Generalizations of the drift Laplace equation in the Heisenberg group and  Grushin-type spaces
       
Authors: Thomas Bieske (Univ. of South Florida,Tampa, FL, USA)
         Keller Blackwell (Stanford Univ., Stanford, CA USA}

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
of 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 the p-Laplace-type
equation while we primarily concentrate on a generalization of the drift term.

Submitted December 29, 2020. Published December 20, 2021.
Math Subject Classifications: 53C17, 35H20, 35A08, 22E25, 17B70.
Key Words: p-Laplace equation; Heisenberg group; Grushin-type plane; fundamental solution.