Document Type
Dissertation
Date of Award
5-31-2021
Degree Name
Doctor of Philosophy in Mathematical Sciences - (Ph.D.)
Department
Mathematical Sciences
First Advisor
Brittany Froese Hamfeldt
Second Advisor
David Shirokoff
Third Advisor
Michael Siegel
Fourth Advisor
Travis Askham
Fifth Advisor
Thomas L. Lewis
Abstract
Fully nonlinear elliptic partial differential equations (PDEs) arise in a number of applications. From mathematical finance to astrophysics, there is a great deal of interest in solving them. Eigenvalue problems for fully nonlinear PDEs with transport boundary conditions are of particular interest as alternative formulations of PDEs that require data to satisfy a solvability condition, which may not be known explicitly or may be polluted by noisy data. Nevertheless, these have not yet been well-explored in the literature. In this dissertation, a convergence framework for numerically solving eigenvalue problems for fully nonlinear PDEs is introduced. In addition, existing two-dimensional methods for nonlinear equations are extended to handle transport boundary conditions and eigenvalue problems. Finally, new techniques are designed to enable appropriate discretization of a large range of fully nonlinear three-dimensional equations.
Recommended Citation
Lesniewski, Jacob, "Eigenvalue problems for fully nonlinear elliptic partial differential equations with transport boundary conditions" (2021). Dissertations. 1519.
https://digitalcommons.njit.edu/dissertations/1519
