Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces
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Author | : Kristen Snyder Childers |
Publisher | : |
Total Pages | : |
Release | : 2011 |
ISBN-10 | : OCLC:778367625 |
ISBN-13 | : |
Rating | : 4/5 (25 Downloads) |
Book Synopsis Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces by : Kristen Snyder Childers
Book excerpt: 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.