Journal: Accepted by Communications on Pure and Applied Mathematics

Key Words: Optimal partial transport; Free boundary

Abstract: 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 the free boundary and studying the second boundary value problem of the Monge-Ampère equation, we obtain the C2,α regularity of the potential function as well as that of the free boundary, thereby resolve an open problem raised by Caffarelli and McCann in \cite{CM}.

Co-author: Shibing Chen,Jiakun Liu,Xu-Jia Wang

Translation or Not: no