Regularity of potential functions of the optimal transportation problem

@inproceedings{Ma2004RegularityOP,
title={Regularity of potential functions of the optimal transportation problem},
author={Xi-Nan Ma and Neil S. Trudinger and Xu-Jia Wang},
year={2004}
}

The potential function to the optimal transportation problem satisfies a partial differential equation of Monge-Ampère type. In this paper we introduce the notion of generalized solution, and prove the existence and uniqueness of generalized solutions to the problem. We also prove the solution is smooth under certain structural conditions on the cost… CONTINUE READING