  This manuscript discusses the approximation of a global maximizer of the
Kantorovich mass transfer problem through the approach of $p$-Laplacian
equation. Using an approximation mechanism, the primal maximization problem can
be transformed into a sequence of minimization problems. By applying the
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 a global maximizer of the primal Kantorovich problem will be
demonstrated.
