A1 Journal article (refereed)
Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces (2024)

Koivu, J., Lučić, D., & Rajala, T. (2024). Approximation by BV-extension Sets via Perimeter Minimization in Metric Spaces. International Mathematics Research Notices, 2024(11), 9359-9375. https://doi.org/10.1093/imrn/rnae048

JYU authors or editors

Publication details

All authors or editors: Koivu, Jesse; Lučić, Danka; Rajala, Tapio

Journal or series: International Mathematics Research Notices

ISSN: 1073-7928

eISSN: 1687-0247

Publication year: 2024

Publication date: 20/03/2024

Volume: 2024

Issue number: 11

Pages range: 9359-9375

Publisher: Oxford University Press (OUP)

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1093/imrn/rnae048

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/94378

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2305.02891

Abstract

We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed BV-extension sets. The extension sets are obtained by minimizing the sum of the perimeter and the measure of the difference between the domain and the set. By earlier results, in PI spaces the minimizers have open representatives with locally quasiminimal surface. We give an example in a PI space showing that the open representative of the minimizer need not be a BVextension domain nor locally John.

Keywords: functional analysis; metric spaces

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2024

Preliminary JUFO rating: 2