Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality

Estibalitz Durand-Cartagena, Sylvester Eriksson-Bique, Riikka Korte, Nageswari Shanmugalingam*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda Jr. We show that these two notions coincide if the measure is doubling and supports a 1-Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a 1-Poincaré inequality, then the metric space supports a Semmes family of curves structure.

Original languageEnglish
Pages (from-to)231-245
Number of pages15
JournalAdvances in Calculus of Variations
Volume14
Issue number2
DOIs
Publication statusPublished - 1 Apr 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • AM-modulus
  • bounded variation

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