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

Year 2023, Volume: 6 Issue: 3, 164 - 175, 15.09.2023

Thomas Bieske , Keller Blackwell

https://doi.org/10.33205/cma.1324774

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

References

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