Continuous Sobolev functions with singularity on arbitrary real-analytic sets

2024/06/06 by Pan, Yifei, Zhang, Yuan
#14E15 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Primary 32C07 #Secondary 46E35

paper · doi:10.48550/arxiv.2406.04544

Abstract

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

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