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Boundary ε-regularity in optimal transportation

Chen, Shibing; Figalli, Alessio

Description

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.

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
URI: http://hdl.handle.net/1885/13661
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2014.12.032

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