带角域边界的距离函数
偏微分方程分析
2019-01-23 v3
摘要
我们研究 中域到其边界的距离函数关于某些非对称范数的正则性。我们允许域的边界具有角点。我们得到了这些距离函数二阶导数的显式公式。此外，我们研究域的脊的广义概念，即到域边界的距离函数的奇点集。我们利用广义曲率概念完全刻画了该脊。
引用
@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}
}
备注
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