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

Electronic Journal of Differential Equations

article

Thomas Bieske¹  Keller Blackwell² 

[1] Department of Mathematics and Statistics University of South Florida Tampa;School of Engineering Stanford University Stanford

关键词: p-Laplace equation;    Heisenberg group;    Grushin-type plane;    fundamental solution.;   

DOI  :  10.58997/ejde.2021.99

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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.

【 授权许可】

CC BY