Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2021-04-01
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Mcode
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Language
en
Pages
15
231-245
231-245
Series
Advances in Calculus of Variations, Volume 14, issue 2
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.Description
Keywords
AM-modulus, bounded variation
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Citation
Durand-Cartagena, E, Eriksson-Bique, S, Korte, R & Shanmugalingam, N 2021, ' Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ', Advances in Calculus of Variations, vol. 14, no. 2, pp. 231-245 . https://doi.org/10.1515/acv-2018-0056