Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665529 | Advances in Mathematics | 2015 | 28 Pages |
Abstract
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 C2C2 uniformly convex domains are C1,αC1,α up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost −x⋅y−x⋅y.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Shibing Chen, Alessio Figalli,