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

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.

Identiferoai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-4237
Date01 January 2011
CreatorsChilders, Kristen Snyder
PublisherScholar Commons
Source SetsUniversity of South Flordia
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceGraduate Theses and Dissertations
Rightsdefault

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