Partial regularity for optimal transport with p-cost away from fixed points

Abstract

We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For Hölder continuous marginals, we prove a $C^{1,\alpha }$-partial regularity result for $T$in the set $\{|T(x)-x|>0\}$.

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