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

## TL;DR

This paper derives fundamental solutions for p-Laplace equations with drift in the Heisenberg group and Grushin spaces, extending classical solutions and focusing on drift term generalizations.

## Contribution

It introduces new fundamental solutions for p-Laplace equations with drift in specific geometric settings, independent of prior p-Laplace generalizations.

## Key findings

- Fundamental solutions for p-Laplace with drift in Heisenberg group
- Fundamental solutions for p-Laplace with drift in Grushin-type spaces
- Results extend classical solutions to more general drift scenarios

## 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.