Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces

2011/12/19 by Thomas Bieske, Bieske, Thomas, Kristen Childers +1
Mathematics · #35H20 #53C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG) #math.AP #math.MG #msc:35H20 #msc:53C17

paper · pdf · doi:10.48550/arxiv.1112.4216

arxiv created 2011/12/19 · arxiv updated 2011/12/20

Abstract

Beals, Gaveau and Greiner (1996) find 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 p-Laplace equation in Grushin-type spaces (Bieske-Gong, 2006) and the Heisenberg group (Capogna, Danielli, Garofalo, 1997). We extend the 2-Laplace-type equation to a 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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