Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.15655 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917503433703424 |
|---|---|
| author | Chen, Shibing Li, Yuanyuan Liu, Jiakun |
| author_facet | Chen, Shibing Li, Yuanyuan Liu, Jiakun |
| contents | In this paper, we investigate optimal (partial) transport problems for which the
target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete
optimal transport problem, we prove that the singular set is locally a smooth
one-dimensional curve away from finitely many points. For the optimal partial
transport problem, we prove that the free boundary is smooth away from finitely
many singular points. In higher dimensions, we formulate two conjectures
concerning the structure of singularities when the target is a non-convex
polytope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15655 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal (partial) transport to non-convex polygonal domains Chen, Shibing Li, Yuanyuan Liu, Jiakun Analysis of PDEs In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport problem, we prove that the singular set is locally a smooth one-dimensional curve away from finitely many points. For the optimal partial transport problem, we prove that the free boundary is smooth away from finitely many singular points. In higher dimensions, we formulate two conjectures concerning the structure of singularities when the target is a non-convex polytope. |
| title | Optimal (partial) transport to non-convex polygonal domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.15655 |