Graduation Year
2011
Document Type
Thesis
Degree
M.A.
Degree Granting Department
Mathematics and Statistics
Major Professor
Thomas Bieske, Ph.D.
Committee Member
Mil´e Krajcevski, Ph.D.
Committee Member
Sherwin Kouchekian, Ph.D.
Keywords
Fundamental Solution, Nonlinear Potential Theory, p-Laplace operator, Partial Differential Equations, 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.
Scholar Commons Citation
Childers, Kristen Snyder, "Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces" (2011). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/3042
