Identifier

etd-11142005-143000

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work we demonstrate how the continuous domain theory can be applied to the theory of nonlinear optimization, particularly to the theory of viscosity solutions. We consider finding the viscosity solution for the Hamilton-Jacobi equation H(x, y) = g(x), with continuous hamiltonian, but with possibly discontinuous right-hand side. We begin by finding a new function space Q(X,L), the space of equivalence classes of quasicontinuous functions from a locally compact set X to a bicontinuous lattice L and we will define on Q(X,L) the qo-topology, which is a variant of classical order topology defined on complete lattices. On this new function space we will show that there exist closed extensions of some differential operators, like the usual gradient and the operator defined by the continuous hamiltonian H. The domain of the closure of the corresponding operator will coincide with the set of viscosity solutions for the Hamilton-Jacobi equation when the hamiltonian is convex in the second argument.

Date

2005

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Jimmie Lawson

Share

COinS