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Full-Text Articles in Physical Sciences and Mathematics
A Maximum Principle In The Engel Group, James Klinedinst
A Maximum Principle In The Engel Group, James Klinedinst
USF Tampa Graduate Theses and Dissertations
In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.
Generalizations Of A Laplacian-Type Equation In The Heisenberg Group And A Class Of Grushin-Type Spaces, Kristen Snyder Childers
Generalizations Of A Laplacian-Type Equation In The Heisenberg Group And A Class Of Grushin-Type Spaces, Kristen Snyder Childers
USF Tampa Graduate Theses and Dissertations
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.