Optimal Transportation on the Hemisphere
نویسندگان
چکیده
In this paper, we study the optimal transportation on the hemisphere, with the cost function c(x, y) = 1 2 d(x, y), where d is the Riemannian distance of the round sphere. The potential function satisfies a Monge-Ampère type equation with natural boundary condition. We obtain the a priori oblique estimate without using any uniform convexity of domains, and in particular for two dimensional case, we obtain the boundary C estimate. Our proof does not depend on the smoothness of densities, which is new even for standard Monge-Ampère equations and optimal transportation on Euclidean spaces.
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