Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces

Bieske, Thomas; Childers, Kristen

doi:10.1090/S0002-9939-2013-11928-3

Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces
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by Thomas Bieske and Kristen Childers PDF

Proc. Amer. Math. Soc. 142 (2014), 989-1003 Request permission

Abstract:

In their 1996 paper, Beals, Gaveau and Greiner found the fundamental solution to a $2$-Laplace-type equation in a class of sub-Riemannian spaces. This solution is related to the well-known fundamental solution to the $\texttt {p}$-Laplace equation in Grushin-type spaces and the Heisenberg group. We extend the $2$-Laplace-type equation to a $\texttt {p}$-Laplace-type equation. We show that the obvious generalization does not have desired properties, but rather, our generalization preserves some natural properties.

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