A note on the weak\(^\ast\) and pointwise convergence of \(\operatorname{BV}\) functions

DOI10.1016/J.NA.2022.113028OpenAlexW3087613770WikidataQ113868536 ScholiaQ113868536MaRDI QIDQ2079661

Lisa Beck, Panu Lahti

Publication date: 30 September 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.09889

zbMATH Keywords

Hausdorff dimensionpointwise convergencefunctions of bounded variationweak star convergenceCantor partvariation measure

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Fine potential theory; fine properties of sets and functions (31C40) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Hausdorff and packing measures (28A78)

Cites Work

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• Regularity of sets with quasiminimal boundary surfaces in metric spaces
• Hitchhiker's guide to the fractional Sobolev spaces
• The fractional Cheeger problem
• Fine properties and a notion of quasicontinuity for BV functions on metric spaces
• Beyond local maximal operators
• Elliptic regularity theory. A first course
• Liftings, Young measures, and lower semicontinuity
• A note on homogeneous Sobolev spaces of fractional order
• Weakly Differentiable Functions

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