Optimal Couplings of Kantorovich-Rubinstein-Wasserstein Lp-distance


  •  Yinfang Shen    

Abstract

We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein Lp-distance (p > 2) (abbreviation:
KRW Lp-distance) in a bounded region of Euclidean plane satisfy a partial differential equation. We can also obtain
the similar results about Monge-Kantorovich problem with more general convex cost functions.



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