REGULARITY FOR SOLUTIONS TO PARABOLIC SYSTEMS AND NONLOCAL MINIMIZATION PROBLEMS

Authors

Joe Geisbauer, University of Nebraska-LincolnFollow

Date of this Version

Spring 4-8-2013

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska-Lincoln In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Mikil Foss. Lincoln, Nebraska: May, 2013

Copyright (c) 2013 Joe Geisbauer

Abstract

The goal of this dissertation is to contribute to both the nonlocal and local settings of regularity within the calculus of variations. We provide analogues of higher differentiability results in the context of Besov spaces for minimizers of nonlocal functionals. We also establish the Holder continuity of solutions to a system of parabolic partial differential equations.

Advisor: Mikil Foss