On the Monge-Kantorovich Mass Transfer Problem in Higher Dimensions

This paper mainly investigates the approximation of a global maximizer of the Monge-Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary. Using an approximation mechanism, the primal maximization problem can be transformed into a sequence of minimization problems. By applying the systematic canonical duality theory, one is able to derive a sequence of analytic solutions for the minimization problems. In the final analysis, the convergence of the sequence to an analytical global maximizer of the primal Monge-Kantorovich problem will be demonstrated.