The distance function from the boundary of a domain with corners
Abstract
We study the regularity of the distance function to the boundary of a domain in , with respect to some asymmetric norms. We allow the boundary of the domain to have corners. We obtain an explicit formula for the second derivative of these distance functions. Furthermore, we study a generalized notion of the ridge of a domain, which is the set of singularities of a distance function to the boundary of the domain. We completely characterize the ridge by using a generalized notion of curvature.
Keywords
Cite
@article{arxiv.1602.03425,
title = {The distance function from the boundary of a domain with corners},
author = {Mohammad Safdari},
journal= {arXiv preprint arXiv:1602.03425},
year = {2019}
}
Comments
The previous title of this article was "Optimal regularity for variational problems with nonsmooth non-strictly convex gradient constraints". Some parts of the previous version are now removed. A more general version of those parts are presented in the article "arXiv:1807.01590". 18 pages