Global ETD Search

1	An extremal problem related to analytic continuation Makhmudov, Olimdjan, Tarkhanov, Nikolai January 2013 (has links) We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations. Extremal problem Euler equations p-Laplace operator mixed problems Mathematics
2	Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces Childers, Kristen Snyder 01 January 2011 (has links) 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. Fundamental Solution Nonlinear Potential Theory Partial Differential Equations p-Laplace operator Sub-Riemannian Geometry American Studies Arts and Humanities Mathematics