REGULARITY FOR SOLUTIONS TO PARABOLIC SYSTEMS AND NONLOCAL MINIMIZATION PROBLEMS
Joe Geisbauer · Lincoln (University of Nebraska) · 2013
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