A note on the weak* and pointwise convergence of BV functions

被引：0

作者：

Beck, Lisa ^{[1
]}

Lahti, Panu ^{[1
,2
]}

机构：

[1] Univ Augsburg, Inst Math, Univ Str 14, D-86159 Augsburg, Germany

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 225卷

关键词：

Functions of bounded variation; Weak star convergence; Pointwise convergence; Variation measure; Cantor part; Hausdorff dimension;

D O I：

10.1016/j.na.2022.113028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study pointwise convergence properties of weakly* convergent sequences {u(i)}(i is an element of N) in BV(R-n). We show that, after passage to a suitable subsequence (not relabeled), we have pointwise convergence u(i)(*)(x) -> u*(x) of the precise representatives for all x is an element of R-n\ E, where the exceptional set E subset of R-n has on the one hand Hausdorff dimension at most n - 1, and is on the other hand also negligible with respect to the Cantor part of |Du|. Furthermore, we discuss the optimality of these results. (c) 2022 Published by Elsevier Ltd.

引用

页数：20

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