Boundary ε-regularity in optimal transportation

Chen, Shibing; Figalli, Alessio

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Boundary ε-regularity in optimal transportation

Date

2015

Authors

Chen, Shibing

Figalli, Alessio

Publisher

Elsevier

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 C2 uniformly convex domains are C1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost −x · y.