Removability of product sets for Sobolev functions in the plane

被引：0
|
作者：
Bindini, Ugo [1 ]
Rajala, Tapio [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland
来源：
ARKIV FOR MATEMATIK | 2023年 / 61卷 / 01期
基金：
芬兰科学院;
关键词：
QUASI-CONFORMAL MAPPINGS;
D O I：
10.4310/ARKIV.2023.v61.n1.a4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study conditions on closed sets C, F subset of R making the product CxF removable or non-removable for W-1,W-p. The main results show that the Hausdorff-dimension of the smaller dimensional component C determines a critical exponent above which the product is removable for some positive measure sets F, but below which the product is not removable for another collection of positive measure totally disconnected sets F. Moreover, if the set C is Ahlfors-regular, the above removability holds for any totally disconnected F.
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页码：67 / 80
页数：14
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