| Title: |
Boundary regularity for the distance functions, and the eikonal equation |
| Authors: |
Nikolov, Nikolai; Thomas, Pascal J. |
| Source: |
J. Geom. Anal. 35 (2025), 230 |
| Publication Year: |
2024 |
| Subject Terms: |
Analysis of PDEs; Complex Variables; 35F20, 35F21, 35B65 |
| Description: |
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.; version 2; to appear in Journal of Geometric Analysis |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2409.01774 |
| Accession Number: |
edsarx.2409.01774 |
| Database: |
arXiv |