Generalizations of the drift Laplace equation in the Heisenberg group and Grushin-type spaces
Texas State University, Department of Mathematics
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.
p-Laplace equation, Heisenberg group, Grushin-type plane, Fundamental solution
Bieske, T., & Blackwell, K. (2021). Generalizations of the drift Laplace equation in the Heisenberg group and Grushin-type spaces. <i>Electronic Journal of Differential Equations, 2021</i>(99), pp. 1-13.