# Distance functions with dense singular sets

created by santilli on 21 Jul 2020

[BibTeX]

preprint

Inserted: 21 jul 2020

Year: 2020

ArXiv: 2007.08959 PDF

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.

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