Chen, Shibing; Figalli, Alessio
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.
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