On the regularity of the maximal function of a BV function

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Lahti, Panu¹ 

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

关键词: Function of bounded variation;    Sobolev function;    Non-centered maximal function;    Quasicontinuity;    Absolute continuity;   

DOI  :  10.1016/j.jde.2021.07.037

来源: Elsevier

【 摘 要 】

We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that if the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent result of Weigt [12], we are in particular able to show that the non-centered maximal function of a set of finite perimeter is a Sobolev function. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free