Weighted Bounded Variation Revisited
Classical Analysis and ODEs
2026-05-19 v2 Functional Analysis
Abstract
In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity and/or a pointwise A1 condition on the weight. Our motivation is twofold: to establish weighted Gagliardo-Nirenberg-Sobolev (GNS) inequalities for BV functions, and to clarify and extend earlier results on weighted BV spaces. Our main contributions include a structure theorem under minimal assumptions (lower semicontinuity), a smooth approximation result, an embedding theorem, a weighted GNS inequality for BV functions, and a corresponding weighted isoperimetric inequality.
Cite
@article{arxiv.2510.14105,
title = {Weighted Bounded Variation Revisited},
author = {Simon Bortz and Matthew Gossett and Joseph Kasel and Kabe Moen},
journal= {arXiv preprint arXiv:2510.14105},
year = {2026}
}
Comments
23 pages. v2 additions suggested by referee