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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 1Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a 1Poincaré inequality, then the metric space supports a Semmes family of curves structure.
Original language  English 

Pages (fromto)  231245 
Number of pages  15 
Journal  Advances in Calculus of Variations 
Volume  14 
Issue number  2 
DOIs  
Publication status  Published  1 Apr 2021 
MoE publication type  A1 Journal articlerefereed 
Keywords
 AMmodulus
 bounded variation
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Dive into the research topics of 'Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1Poincaré inequality'. Together they form a unique fingerprint.Projects
 1 Finished

Parabolic flows with variational methods
Korte, R., Pacchiano Camacho, C., Buffa, V., Myyryläinen, K., Takala, T., Kurki, E., Weigt, J., Evdoridis, S. & Vestberg, M.
01/09/2017 → 31/08/2021
Project: Academy of Finland: Other research funding