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

Yanhua Wu; Xiaojun Lu

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arXiv · 1609.02813

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

Yanhua Wu·Xiaojun Lu

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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.

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Yanhua Wu, Xiaojun Lu. 2016-09-09. Analytic solutions for the approximated Kantorovich mass transfer problems by $p$-Laplacian approach. https://arxiv.org/abs/1609.02813

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