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arXiv · 2510.14105

Weighted Bounded Variation Revisited

Simon Bortz·Matthew Gossett·Joseph Kasel·Kabe Moen
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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.

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Simon Bortz, Matthew Gossett, Joseph Kasel, Kabe Moen. 2026-05-15. Weighted Bounded Variation Revisited. https://arxiv.org/abs/2510.14105

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