Analytic solutions for the approximated Kantorovich mass transfer problems by $p$-Laplacian approach

Abstract

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.

11 pages, 0 figure. arXiv admin note: text overlap with arXiv:1607.06554, arXiv:1608.03385

References in corpus (1)

• Optimal transport maps in Monge-Kantorovich problem