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

Michael Goldman; Lukas Koch

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arXiv · 2407.08846

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

Michael Goldman·Lukas Koch

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Abstract

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

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Michael Goldman, Lukas Koch. 2024-07-11. Partial regularity for optimal transport with p-cost away from fixed points. https://arxiv.org/abs/2407.08846

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