Fine properties of monotone maps arising in optimal transport for non-quadratic costs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917680969154560 |
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| author | Gutierrez, Cristian E. Montanari, Annamaria |
| author_facet | Gutierrez, Cristian E. Montanari, Annamaria |
| contents | The cost functions considered are $c(x,y)=h(x-y)$, where $h\in C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and establish that they are single-valued almost everywhere. Further consequences are then deduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00193 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fine properties of monotone maps arising in optimal transport for non-quadratic costs Gutierrez, Cristian E. Montanari, Annamaria Analysis of PDEs Functional Analysis 49Q22, 47H05, 46T20 The cost functions considered are $c(x,y)=h(x-y)$, where $h\in C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and establish that they are single-valued almost everywhere. Further consequences are then deduced. |
| title | Fine properties of monotone maps arising in optimal transport for non-quadratic costs |
| topic | Analysis of PDEs Functional Analysis 49Q22, 47H05, 46T20 |
| url | https://arxiv.org/abs/2208.00193 |