Global $W^{2,1+\hat{I}\mu }$ regularity for potentials of optimal transport of non-convex planar domains

Shengnan Hu, Yuanyuan Li

In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in ${\mathbb{R}}^2$. We show a global $W^{2,1+\hat{I}\mu }$ estimate for potential…