Sobolev extensions over Cantor-cuspidal graphs

Pekka Koskela, Zheng Zhu

For a continuous function $f:\mathbb{R}\to \mathbb{R}$, define the corresponding graph by setting \[Γ_f := {(x1, f(x1)) : x_1\in\mathbb{R}} .\] In this paper, we study the Sobolev e…