Indecomposable sets of finite perimeter in doubling metric measure spaces
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202003092338Use this for linking
Review status
Peer reviewed
ISSN
0944-2669
DOI
https://doi.org/10.1007/s00526-020-1725-7
Language
English
Published in
Calculus of Variations and Partial Differential Equations
Citation
- 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
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Funder(s)
Research Council of Finland
Research Council of Finland
Research Council of Finland
Research Council of Finland
Funding program(s)
Academy Research Fellow, AoF
Centre of Excellence, AoF
Research costs of Academy Research Fellow, AoF
Academy Project, AoF
Akatemiatutkija, SA
Huippuyksikkörahoitus, SA
Akatemiatutkijan tutkimuskulut, SA
Akatemiahanke, SA
Additional information about funding
Open access funding provided by University of Jyväskylä (JYU). The first named author acknowledges ERC Starting Grant 676675 FLIRT. The second and third named authors are partially supported by the Academy of Finland, Projects 274372, 307333, 312488, and 314789.
Copyright© 2020 the Authors