Calculus of Variations and Geometric Measure Theory
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M. Santilli

Distance functions with dense singular sets

created by santilli on 21 Jul 2020
modified on 14 Jun 2021

[BibTeX]

Published Paper

Inserted: 21 jul 2020
Last Updated: 14 jun 2021

Journal: Comm. Partial Differential Equations
Year: 2021
Doi: https://doi.org/10.1080/03605302.2021.1871623

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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