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In this work we present a numerical method for the Optimal MassTransportation problem. Optimal Mass Transportation (OT) is an active researchfield in mathematics.It has recently led to significant theoretical results aswell as applications in diverse areas. Numerical solution techniques for the OTproblem remain underdeveloped. The solution is obtained by solving the secondboundary value problem for the MA equation, a fully nonlinear elliptic partialdifferential equation (PDE). Instead of standard boundary conditions theproblem has global state constraints. These are reformulated as a tractablelocal PDE. We give a proof of convergence of the numerical method, using thetheory of viscosity solutions. Details of the implementation and a fastsolution method are provided in the companion paper arXiv:1208.4870.

A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem