Boundary Ε-regularity in Optimal Transportation
نویسندگان
چکیده
We develop an ε-regularity theory at the boundary for a general class of MongeAmpère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C uniformly convex domains are C up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost −x · y.
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