Degree Granting Department
Mathematics and Statistics
Thomas Bieske, Ph.D.
Mil´e Krajcevski, Ph.D.
Sherwin Kouchekian, Ph.D.
Fundamental Solution, Nonlinear Potential Theory, p-Laplace operator, Partial Differential Equations, Sub-Riemannian Geometry
In , 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  and the Heisenberg group . In this thesis, we look to generalize the work in  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). Graduate Theses and Dissertations.