Differentiability of monotone maps related to non-quadratic costs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929519600861184 |
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| author | Gutiérrez, Cristian E. Montanari, Annamaria |
| author_facet | Gutiérrez, Cristian E. Montanari, Annamaria |
| contents | The cost functions considered are $c(x,y)=h(x-y)$, with $h\in C^2(R^n)$, homogeneous of degree $p\geq 2$, with positive definite Hessian in the unit sphere. We consider monotone maps $T$ concerning that cost and establish local $L^\infty$-estimates of $T$ minus affine functions, which are applied to obtain differentiability properties of $T$ a.e. It is also shown that these maps are related to maps of bounded deformation, and further, differentiability and Hölder continuity properties are derived. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_19127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiability of monotone maps related to non-quadratic costs Gutiérrez, Cristian E. Montanari, Annamaria Analysis of PDEs Functional Analysis 49Q22, 47H05, 35J96 The cost functions considered are $c(x,y)=h(x-y)$, with $h\in C^2(R^n)$, homogeneous of degree $p\geq 2$, with positive definite Hessian in the unit sphere. We consider monotone maps $T$ concerning that cost and establish local $L^\infty$-estimates of $T$ minus affine functions, which are applied to obtain differentiability properties of $T$ a.e. It is also shown that these maps are related to maps of bounded deformation, and further, differentiability and Hölder continuity properties are derived. |
| title | Differentiability of monotone maps related to non-quadratic costs |
| topic | Analysis of PDEs Functional Analysis 49Q22, 47H05, 35J96 |
| url | https://arxiv.org/abs/2409.19127 |