Regularity Results for Potential Functions of the Optimal Transportation Problem on Spheres and Related Hessian Equations
In this thesis, results will be presented that pertain to the global regularity of solutions to a class of boundary value problems closely related to the Optimal Transportation Equation. Ultimately, analogies to the global regularity result presented in [TW06] for the Optimal Transportation Problem to this new fully-nonlinear elliptic boundary value problem will be presented and proven. It will also be shown that the A3w condition (first presented in [MTW05]) is also necessary for global...[Show more]
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