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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.10013 |
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| _version_ | 1866915670559555584 |
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| author | Safdari, Mohammad |
| author_facet | Safdari, Mohammad |
| contents | We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also explicitly compute the distance function in a collection of examples and observe the new interesting phenomena that arise for such distance functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The distance to the boundary with respect to the Minkowski functional of a polytope Safdari, Mohammad Metric Geometry Analysis of PDEs We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also explicitly compute the distance function in a collection of examples and observe the new interesting phenomena that arise for such distance functions. |
| title | The distance to the boundary with respect to the Minkowski functional of a polytope |
| topic | Metric Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.10013 |