Electron. J. Differential Equations, Vol. 2021 (2021), No. 99, pp. 1-13.

Generalizations of the drift Laplace equation in the Heisenberg group and Grushin-type spaces

Thomas Bieske, Keller Blackwell

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.
DOI: https://doi.org/10.58997/ejde.2021.99

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Thomas Bieske
Department of Mathematics and Statistics
University of South Florida
Tampa, FL 33620-5700, USA
email: tbieske@usf.edu
Keller Blackwell
School of Engineering
Stanford University
Stanford, CA 94305, USA
email: kellerb@stanford.edu

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