Sobolev extensions over Cantor-cuspidal graphs

2023/12/15 by Koskela, Pekka, Zhu, Zheng
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2312.09497

Abstract

For a continuous function f:ℝ→ℝ, define the corresponding graph by setting Γ_f := (x1, f(x1)) : x₁∈ℝ . In this paper, we study the Sobolev extension property for the upper and lower domains over the graph Γ_ψ^αc for ψ^α_c(x₁):=d(x₁, \mathcal C)^α, where \mathcal C is the classical ternary Cantor set in the unit interval and α∈(0, 1).

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