Type of Document 
Dissertation 
Author 
Cazacu, Rodica

Author's Email Address 
rcazac1@lsu.edu 
URN 
etd11142005143000 
Title 
Quasicontinuous Derivatives and Viscosity Functions 
Degree 
Doctor of Philosophy (Ph.D.) 
Department 
Mathematics 
Advisory Committee 
Advisor Name 
Title 
Jimmie Lawson 
Committee Chair 
Charles Monlezun 
Committee Member 
Daniel C. Cohen 
Committee Member 
Frank Neubrander 
Committee Member 
William Adkins 
Committee Member 
Suresh Rai 
Dean's Representative 

Keywords 
 bicontinuous lattice
 quasicontinuous
 viscosity solution
 approximate function
 domain theory

Date of Defense 
20051110 
Availability 
unrestricted 
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 HamiltonJacobi equation H(x, y) = g(x), with continuous hamiltonian, but with possibly discontinuous righthand 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 qotopology, 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 HamiltonJacobi equation when the hamiltonian is convex in the second argument.

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