10 citations · 29 across the 32 of their papers we have counts for
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math.AP2019★ 1 cited
Regularity of free boundaries in optimal transportation
Shibing Chen, Jiakun Liu
In this paper, we obtain some regularities of the free boundary in optimal transportation with the quadratic cost. Our first result is about the regularity of the free bo…
math.AP2019★ 2 cited
regularity of free boundaries in optimal transportation
Shibing Chen, Jiakun Liu, Xu-Jia Wang
The regularity of the free boundary in optimal transportation is equivalent to that of the potential function along the free boundary. By establishing new geometric estimates of th…
math.AP2019
Global regularity of optimal mappings in non-convex domains
Shibing Chen, Jiakun Liu, Xu-Jia Wang
In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a…