6 papers · 1 filter
Optimal (partial) transport to non-convex polygonal domains
Shibing Chen, Yuanyuan Li, Jiakun Liu
In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport pro…
Global regularity in the Monge-Ampère obstacle problem
Shibing Chen, Jiakun Liu, Xianduo Wang
In this paper, we establish the global estimate for the Monge-Ampère obstacle problem: , where and are positive cont…
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…
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…
-Brunn-Minkowski inequality for
Shibing Chen, Yong Huang, Qi-rui Li +1
Kolesnikov-Milman [9] established a local -Brunn-Minkowski inequality for Based on their local uniqueness results for the -Minkowski proble…
Boundary regularity for the second boundary-value problem of Monge-Ampère equations in dimension two
Shibing Chen, Jiakun Liu, Xu-Jia Wang
In this paper, we introduce an iteration argument to prove that a convex solution to the Monge-Ampère equation $\mbox{det } D^2 u =f $ in dimension two subject to the natural bound…