Boundary regularity for the distance functions, and the eikonal equation

par Pascal Thomas (IMT)

lundi 28 avr. 2025, 14:00 → 15:00 Europe/Paris

Salle Pellos (1R2-207)

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.

https://arxiv.org/abs/2409.01774