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.

中文翻译：

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具有稠密奇异集的距离函数

摘要

我们从一个 ${\mathcal{C}}^1$-超曲面在内球条件方面，我们解决了 Eikonal 方程的粘度解存在的问题，其奇异集（即非可微点集）不是无处稠密的。