Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces

Thomas Bieske; Keller Blackwell

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arXiv · 1910.04580

Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces

Thomas Bieske·Keller Blackwell

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Abstract

Beals, Gaveau, and Greiner in 1996 establish a formula for the fundamental solution to the Laplace equation with drift term in Grushin-type planes. The first author and Childers in 2013 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.

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Thomas Bieske, Keller Blackwell. 2019-10-09. Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces. https://arxiv.org/abs/1910.04580

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