Optimal transport to non-convex polyhedral domains
Shibing Chen, Qi-Rui Li, Yuanyuan Li, Jiakun Liu, Xiaotian Wu
Abstract
We study optimal transport with a non-convex polyhedral target in Rn. The closure of the singular set is locally a smooth hypersurface outside a relatively closed set of Hausdorff dimension at most n-2. For partial transport between domains separated by a hyperplane, the source free boundary has the same regularity.
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