On uniqueness of an optimal solution to the Kantorovich problem with density constraints
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911758154727424 |
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| author | Popova, Svetlana |
| author_facet | Popova, Svetlana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On uniqueness of an optimal solution to the Kantorovich problem with density constraints Popova, Svetlana Functional Analysis Probability 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. |
| title | On uniqueness of an optimal solution to the Kantorovich problem with density constraints |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2401.07067 |