A compactness result for BV functions in metric spaces

2018/03/20 by Sebastiano Don, Davide Vittone, Don, Sebastiano +1 · 1 citation
Engineering · Mathematics · #26B30 #26D10 #46E35 #53C17 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Bounded function #Carnot cycle #Compact space #Computer science #Convex metric space #Discrete mathematics #Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Injective metric space #Mathematical analysis #Mathematics #Metric (unit) #Metric Geometry (math.MG) #Metric space #Nonlinear Partial Differential Equations #Physics #Pure mathematics #Space (punctuation) #Uniform continuity #math.FA #math.MG #msc:26B30 #msc:26D10 #msc:46E35 #msc:53C17

paper · pdf · doi:10.48550/arxiv.1803.07545

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2018/03/20 · arxiv created 2018/03/21 · arxiv updated 2018/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We prove a compactness result for bounded sequences (u_j)_j of functions with bounded variation in metric spaces (X,d_j) where the space X is fixed but the metric may vary with j. We also provide an application to Carnot-Carathéodory spaces.

Cited by

• Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces

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