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

doi:10.1515/acv-2018-0056

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 journal › Article › Scientific › peer-review

8 Citations (Scopus)

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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 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 language	English
Pages (from-to)	231-245
Number of pages	15
Journal	Advances in Calculus of Variations
Volume	14
Issue number	2
DOIs	https://doi.org/10.1515/acv-2018-0056
Publication status	Published - 1 Apr 2021
MoE publication type	A1 Journal article-refereed

Keywords

AM-modulus
bounded variation

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10.1515/acv-2018-0056

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequalityAccepted author manuscript, 337 KB

Cite this

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keywords = "AM-modulus, bounded variation",

author = "Estibalitz Durand-Cartagena and Sylvester Eriksson-Bique and Riikka Korte and Nageswari Shanmugalingam",

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doi = "10.1515/acv-2018-0056",

language = "English",

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Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality. / Durand-Cartagena, Estibalitz; Eriksson-Bique, Sylvester; Korte, Riikka et al.
In: Advances in Calculus of Variations, Vol. 14, No. 2, 01.04.2021, p. 231-245.

Research output: Contribution to journal › Article › Scientific › peer-review

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T1 - Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality

AU - Durand-Cartagena, Estibalitz

AU - Eriksson-Bique, Sylvester

AU - Korte, Riikka

AU - Shanmugalingam, Nageswari

PY - 2021/4/1

Y1 - 2021/4/1

N2 - 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.

AB - 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.

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KW - bounded variation

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DO - 10.1515/acv-2018-0056

M3 - Article

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VL - 14

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EP - 245

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

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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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Parabolic flows with variational methods

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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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Parabolic flows with variational methods

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