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arXiv · 2401.07067

On uniqueness of an optimal solution to the Kantorovich problem with density constraints

Svetlana Popova
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Abstract

We study optimal transportation problems with constraints on densities of transport plans. We obtain a sharp condition for the uniqueness of an optimal solution to the Kantorovich problem with density constraints, namely that the Borel measurable cost function $h(x, y)$ satisfies the following non-degeneracy condition: $h(x, y)$ can not be expressed as a sum of functions $u(x) + v(y)$ on a set of positive measure.

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Svetlana Popova. 2024-01-13. On uniqueness of an optimal solution to the Kantorovich problem with density constraints. https://arxiv.org/abs/2401.07067

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