PDE Seminar Abstracts

Optimal transportation on the hemisphere

Jiakun Liu
University of Wollongong
Mon 18th Apr 2016, 2-3pm, Carslaw Room 829 (AGR)


In this talk, we first give a brief introduction to the optimal transportation problem. Then we study the optimal transportation on the hemisphere with the cost function c(x,y) = d2(x,y)2, where d is the Riemannian distance of the round sphere. The potential function satisfies a Monge-Ampere type equation with a natural boundary condition. In this critical case, the hemisphere does not satisfy the c-convexity assumption. We obtain the a priori oblique derivative estimate, and in the special case of dimension two, we obtain the boundary C2 estimate. Our proof does not require the smoothness of densities.

This is joint work with S.-Y. Alice Chang and Paul Yang.