Global $W^{2,1+ε}$ regularity for potentials of optimal transport of non-convex planar domains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911393760935936 |
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| author | Hu, Shengnan Li, Yuanyuan |
| author_facet | Hu, Shengnan Li, Yuanyuan |
| contents | In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in $\mathbb{R}^2$. We show a global $W^{2,1+ε}$ estimate for potentials of optimal transport. Our method applies to a more general class of domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16707 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global $W^{2,1+ε}$ regularity for potentials of optimal transport of non-convex planar domains Hu, Shengnan Li, Yuanyuan Analysis of PDEs In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in $\mathbb{R}^2$. We show a global $W^{2,1+ε}$ estimate for potentials of optimal transport. Our method applies to a more general class of domains. |
| title | Global $W^{2,1+ε}$ regularity for potentials of optimal transport of non-convex planar domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.16707 |