Global W^2,p Regularity in Optimal Transport

2026/07/27 by Shibing Chen, Yuanyuan Li, Xianduo Wang
#math.AP

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Abstract

In this paper we establish global W^2,p estimates for the convex potential functions of quadratic optimal transport between bounded convex domains. The source and target densities are assumed only to be continuous and bounded away from zero and infinity, and no regularity is imposed on the domain boundaries.

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• Boundary regularity of optimal transport maps on convex domains
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