Strict and pointwise convergence of BV functions in metric spaces

2016/12/19 by Panu Lahti, Lahti, Panu · 1 citation
Mathematics · #26B30 #28A20 #30L99 #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #math.MG #msc:26B30 #msc:28A20 #msc:30L99

paper · pdf · doi:10.48550/arxiv.1612.06447

arXiv admin note: text overlap with arXiv:1612.06286

arxiv created 2016/12/19 · openalex publication_date 2016/12/19 · arxiv updated 2016/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of a metric space X equipped with a doubling measure that supports a Poincaré inequality, we show that if u_i→ u strictly in BV(X), i.e. if u_i→ u in L¹(X) and \Vert Du_i\Vert(X)→\Vert Du\Vert(X), then for a subsequence (not relabeled) we have \widetildeu_i(x)→ \widetildeu(x) for \mathcal H-almost every x∈ X∖ S_u.

Citations

• Quasiconformal maps in metric spaces with controlled geometry
• A Federer-style characterization of sets of finite perimeter on metric spaces

Cited by

• Existence theory for linear-growth variational integrals with signed measure data

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