On the regularity of the maximal function of a BV function
Classical Analysis and ODEs
2020-07-14 v1
Abstract
We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{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, we are in particular able to show that the non-centered maximal function of a set of finite perimeter is a Sobolev function.
Cite
@article{arxiv.2007.05752,
title = {On the regularity of the maximal function of a BV function},
author = {Panu Lahti},
journal= {arXiv preprint arXiv:2007.05752},
year = {2020}
}