A1 Journal article (refereed)
Indecomposable sets of finite perimeter in doubling metric measure spaces (2020)

Bonicatto, P., Pasqualetto, E., & Rajala, T. (2020). Indecomposable sets of finite perimeter in doubling metric measure spaces. Calculus of Variations and Partial Differential Equations, 59(2), Article 63. https://doi.org/10.1007/s00526-020-1725-7

JYU authors or editors

Publication details

All authors or editors: Bonicatto, Paolo; Pasqualetto, Enrico; Rajala, Tapio

Journal or series: Calculus of Variations and Partial Differential Equations

ISSN: 0944-2669

eISSN: 1432-0835

Publication year: 2020

Volume: 59

Issue number: 2

Article number: 63

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00526-020-1725-7

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68103

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1907.10869

Abstract

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak (1,1)-Poincaré inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.

Keywords: differential geometry; calculus of variations; measure theory; metric spaces

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2