Sobolev Extensions over Cantor-Cuspidal Graphs

Pekka Koskela; Zheng Zhu

doi:10.1007/s10958-024-07145-6

Sobolev Extensions over Cantor-Cuspidal Graphs

Pekka Koskela
, Zheng Zhu^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Jyväskylä

Research output: Contribution to journal › Article › peer-review

Abstract

For a continuous function f : R →R we define the corresponding graph by setting Γ_f ≔ {(x₁, f(x₁)) : x₁ ∈ R}. We give the optimal Sobolev extension properties for the upper and lower domains corresponding to the graph Γψ_c_α for ψ_c^α (x₁) = d(x₁, C)α, where C is the classical ternary Cantor set in the unit interval and α ∈ (0, 1).

Original language	English
Pages (from-to)	706-723
Number of pages	18
Journal	Journal of Mathematical Sciences (United States)
Volume	281
Issue number	5
DOIs	https://doi.org/10.1007/s10958-024-07145-6
State	Published - Jun 2024

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title = "Sobolev Extensions over Cantor-Cuspidal Graphs",

abstract = "For a continuous function f : R →R we define the corresponding graph by setting Γf ≔ \{(x1, f(x1)) : x1 ∈ R\}. We give the optimal Sobolev extension properties for the upper and lower domains corresponding to the graph Γψcα for ψcα (x1) = d(x1, C)α, where C is the classical ternary Cantor set in the unit interval and α ∈ (0, 1).",

author = "Pekka Koskela and Zheng Zhu",

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PY - 2024/6

Y1 - 2024/6

N2 - For a continuous function f : R →R we define the corresponding graph by setting Γf ≔ {(x1, f(x1)) : x1 ∈ R}. We give the optimal Sobolev extension properties for the upper and lower domains corresponding to the graph Γψcα for ψcα (x1) = d(x1, C)α, where C is the classical ternary Cantor set in the unit interval and α ∈ (0, 1).

AB - For a continuous function f : R →R we define the corresponding graph by setting Γf ≔ {(x1, f(x1)) : x1 ∈ R}. We give the optimal Sobolev extension properties for the upper and lower domains corresponding to the graph Γψcα for ψcα (x1) = d(x1, C)α, where C is the classical ternary Cantor set in the unit interval and α ∈ (0, 1).

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M3 - 文章

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JO - Journal of Mathematical Sciences (United States)

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ER -

Sobolev Extensions over Cantor-Cuspidal Graphs

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