Honors Program
Document Type
Thesis
Date of this Version
3-2022
Citation
Pieper, M. 2022. Existence and Uniqueness of Minimizers for a Nonlocal Variational Problem. Honors Undergraduate Thesis. University of Nebraska-Lincoln
Abstract
Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of kernel and boundary conditions.
Included in
Analysis Commons, Gifted Education Commons, Higher Education Commons, Other Applied Mathematics Commons, Other Education Commons, Other Mathematics Commons, Partial Differential Equations Commons
Comments
Copyright Michael Pieper 2022.