Partial regularity of optimal transport with Coulomb cost
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911088844472320 |
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| author | Friesecke, Gero Ried, Tobias |
| author_facet | Friesecke, Gero Ried, Tobias |
| contents | We prove that for two-marginal optimal transport with Coulomb cost, the optimal map is a $C^{1,α}$ diffeomorphism outside a closed set of Lebesgue measure zero provided the marginals are $α$-Hölder continuous and bounded away from zero and infinity. Excluding a set of measure zero is necessary as optimal maps for the Coulomb cost have long been known to exhibit jump singularities across codimension $1$ surfaces (even for smooth marginals on convex domains). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial regularity of optimal transport with Coulomb cost Friesecke, Gero Ried, Tobias Analysis of PDEs Mathematical Physics 49Q22, 35B65 We prove that for two-marginal optimal transport with Coulomb cost, the optimal map is a $C^{1,α}$ diffeomorphism outside a closed set of Lebesgue measure zero provided the marginals are $α$-Hölder continuous and bounded away from zero and infinity. Excluding a set of measure zero is necessary as optimal maps for the Coulomb cost have long been known to exhibit jump singularities across codimension $1$ surfaces (even for smooth marginals on convex domains). |
| title | Partial regularity of optimal transport with Coulomb cost |
| topic | Analysis of PDEs Mathematical Physics 49Q22, 35B65 |
| url | https://arxiv.org/abs/2508.01756 |