The Cheeger problem in abstract measure spaces

Author:

Franceschi Valentina1ORCID,Pinamonti Andrea2,Saracco Giorgio3ORCID,Stefani Giorgio4ORCID

Affiliation:

1. Dipartimento di Matematica “Tullio Levi Civita” Università di Padova Padova PD Italy

2. Dipartimento di Matematica Università di Trento Povo Italy

3. Dipartimento di Matematica e Informatica “Ulisse Dini” Università di Firenze Firenze FI Italy

4. Scuola Internazionale Superiore di Studi Avanzati (SISSA) Trieste TS Italy

Abstract

AbstractWe consider nonnegative ‐finite measure spaces coupled with a proper functional that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter.

Funder

Università degli Studi di Trento

Horizon 2020

Istituto Nazionale di Alta Matematica "Francesco Severi"

Publisher

Wiley

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Non-local BV functions and a denoising model with L 1 fidelity;Advances in Calculus of Variations;2024-01-30

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