Regularity estimates for elliptic equations involving fractional Neumann boundary conditions
Date
2024-08
Authors
Haeuser, Mitchell
Major Professor
Advisor
Stinga, Pablo Raúl
Herzog, David
Nguyen, Xuan Hien
Parshad, Rana
Weber, Eric
Committee Member
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Altmetrics
Abstract
We prove regularity estimates for elliptic equations involving fractional Neumann boundary conditions. In particular, we consider solutions which are harmonic in a Lipschitz domain with a fractional normal derivative boundary condition. To establish various estimates, we utilize the extension problem characterization for the normal derivative, and develop a De Giorgi type theory for our case. In total, we prove interior and boundary Schauder estimates for the aforementioned solutions.
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Type
dissertation