Graduation Year

2011

Document Type

Thesis

Degree

M.A.

Degree Granting Department

Mathematics and Statistics

Major Professor

Thomas Bieske

Keywords

Fundamental Solution, Nonlinear Potential Theory, Partial Differential Equations, p-Laplace operator, Sub-Riemannian Geometry

Abstract

In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.

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