, Volume 177, Issue 2, pp 151-183
Date: 15 Mar 2005

Regularity of Potential Functions of the Optimal Transportation Problem

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

Communicated by L. Ambrosio