English

Distance functions with dense singular sets

Analysis of PDEs 2022-04-12 v2

Abstract

We characterize the denseness of the singular set of the distance function from a C1\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.

Cite

@article{arxiv.2007.08959,
  title  = {Distance functions with dense singular sets},
  author = {Mario Santilli},
  journal= {arXiv preprint arXiv:2007.08959},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-23T17:11:45.625Z