一类Grushin型空间中四元数上漂移Laplace方程的推广
Generalizations of the Drift Laplace Equation over the Quaternions in a Class of Grushin-Type Spaces
摘要：
Beals、Gaveau和Greiner在1996年建立了Grushin型平面上带漂移项的拉普拉斯方程的基本解公式。第一作者和Childers在2013年通过调用包含这些公式的p-Laplace型推广扩展了这些结果，而作者探索了具有漂移项的p-Laplace方程的不同自然推广，也包含这些公式。在这两种情况下，漂移项都位于复域中。我们通过考虑四元数领域中的漂移项来扩展这些结果，并表明我们的解决方案在p趋于无穷大的限制下是稳定的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
