Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces

Authors : Thomas BİESKE, Keller BLACKWELL

Pages : 164-175

Doi:10.33205/cma.1324774

View : 50 | Download : 38

Publication Date : 2023-09-15

Article Type : Research Paper

Abstract :Beals, Gaveau, and Greiner established a formula for the fundamental solution to the Laplace equation with drift term in Grushin-type planes. The first author and Childers expanded these results by invoking a p-Laplace type generalization that encompasses these formulas while the authors explored a different natural generalization of the p-Laplace equation with drift term that also encompasses these formulas. In both, the drift term lies in the complex domain. We extend these results by considering a drift term in the quaternion realm and show our solutions are stable under limits as p tends to infinity.
Keywords : p Laplace equation, Grushin type plane, Grushin type spaces