Boundary ε-regularity in optimal transportation
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.
|Collections||ANU Research Publications|
|Source:||Advances in Mathematics|
|01 Chen and Figalli Boundary e regularity 2015.pdf||264.89 kB||Adobe PDF|
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