Distance functions with dense singular sets

Abstract

We characterize the denseness of the singular set of the distance function from a ${\mathcal{C}}^1$-hypersurface in terms of an inner ball condition and we address the problem of the existence of viscosity solutions of the Eikonal equation whose singular set (i.e. set of non-differentiability points) is not no-where dense.

7 pages. In v2 we correct a couple of minor typos. Submitted

Cited by in corpus (2)

• Delta-convex structure of the singular set of distance functions
• Regularity of distance functions from arbitrary closed sets