Continuous Sobolev functions with singularity on arbitrary real-analytic sets

Abstract

Near every point of a real-analytic set in ${\mathbb{R}}^n$, we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W_{loc}^{1,1}$ such that their weak derivatives have (removable) singularity precisely on that set.

arXiv comment9 pages