Strict and pointwise convergence of BV functions in metric spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Lahti, Panu¹ 

[1] Univ Cincinnati, Dept Math Sci, 4199 French Hall West,2815 Commons Way, Cincinnati, OH 45221 USA

关键词: Metric measure space;    Bounded variation;    Strict convergence;    Pointwise convergence;    Uniform convergence;    Codimension one Hausdorff measure;   

DOI  :  10.1016/j.jmaa.2017.06.010

来源: Elsevier

【 摘 要 】

Consider a metric space X that is equipped with a doubling measure and supports a Poincare inequality. We show that if u(i) -> u strictly in BV(X), i.e. if u(i) -> u in L-1(X) and parallel to Du(i)parallel to(X) -> parallel to Du parallel to(X), then for a subsequence (not relabeled) we have (u) over tilde (i)(x) -> (u) over tilde (x) for H-almost every x is an element of X \ S-u. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free