2019/10/09 by Thomas Bieske, Bieske, Thomas, Keller Blackwell +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1910.04580
openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.