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On the Monge-Kantorovich Mass Transfer Problem in Higher Dimensions

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Abstract

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.

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Acknowledgements

The author thanks the anonymous referees for their careful reading of the manuscript and their many insightful comments.

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Correspondence to Xiao Jun Lu.

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Lu, X.J. On the Monge-Kantorovich Mass Transfer Problem in Higher Dimensions. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-2628-x

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  • DOI: https://doi.org/10.1007/s10114-024-2628-x

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