The distance to the boundary with respect to the Minkowski functional of a polytope

Abstract

We study the regularity of the distance function to the boundary of a domain in ${\mathbb{R}}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also explicitly compute the distance function in a collection of examples and observe the new interesting phenomena that arise for such distance functions.

arXiv comment28 pages