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Regularity For Solutions To Parabolic Systems And Nonlocal Minimization Problems, Joe Geisbauer
Regularity For Solutions To Parabolic Systems And Nonlocal Minimization Problems, Joe Geisbauer
Department of Mathematics: Dissertations, Theses, and Student Research
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