A note on the weak* and pointwise convergence of BV functions

  • We study pointwise convergence properties of weakly* converging sequences {ui}i∈N in BV(Rn). We show that, after passage to a suitable subsequence (not relabeled), we have pointwise convergence u∗i(x)→u∗(x) of the precise representatives for all x∈Rn∖E, where the exceptional set E⊂Rn has on the one hand Hausdorff dimension at most n−1, and is on the other hand also negligible with respect to the Cantor part of |Du|. Furthermore, we discuss the optimality of these results.

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Metadaten
Author:Lisa BeckGND, Panu Lahti
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/79707
URL:https://arxiv.org/abs/2009.09889
Publisher:arXiv
Type:Preprint
Language:English
Year of first Publication:2020
Publishing Institution:Universität Augsburg
Release Date:2020/09/24
Issue:2009.09889
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht