(1) Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT, 0200, Australia
Abstract:
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.
