Regularity of Potential Functions of the Optimal Transportation Problem
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- Ma, XN., Trudinger, N. & Wang, XJ. Arch. Rational Mech. Anal. (2005) 177: 151. doi:10.1007/s00205-005-0362-9
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.