Published Paper
Inserted: 12 dec 2014
Last Updated: 19 aug 2024
Journal: Adv. Math.
Year: 2015
Abstract:
We develop an $\epsilon$-regularity theory at the boundary for a general class of Monge-Amp\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\"older densities supported on $C^2$ uniformly convex domains are $C^{1,\alpha}$ up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost $-x\cdot y$.
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