Calculus of Variations and Geometric Measure Theory
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S. Chen - A. Figalli

Boundary \epsilon-regularity in optimal transportation

created by figalli on 12 Dec 2014
modified on 13 Dec 2014


Accepted Paper

Inserted: 12 dec 2014
Last Updated: 13 dec 2014

Journal: Adv. Math.
Year: 2014


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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