On the regularity of the maximal function of a BV function

[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.

[发布日期] 2021-11-05

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