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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2409.01774 |
| Etiquetas: |
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- We study the gain in regularity of the distance to the boundary of a domain in $\mathbb R^m$. In particular, we show that if the signed distance function happens to be merely differentiable in a neighborhood of a boundary point, it and the boundary have to be $\mathcal C^{1,1}$ regular. Conversely, we study the regularity of the distance function under regularity hypotheses of the boundary. Along the way, we point out that any solution to the eikonal equation, differentiable everywhere in a domain of the Euclidean space, admits a gradient which is locally Lipschitz.