Article ID Journal Published Year Pages File Type
4665529 Advances in Mathematics 2015 28 Pages PDF
Abstract

We develop an ε  -regularity theory at the boundary for a general class of Monge–Ampère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C2C2 uniformly convex domains are C1,αC1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost −x⋅y−x⋅y.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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