2024

Koskela, Pekka; Zhu, Zheng

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 Γψα c for ψα c (x1) = d(x1, C )α, where C is the classical ternary Cantor set in the unit interval and α ∈ (0, 1). Bibliography: 12 titles. Illustrations: 2 figures