We consider nonnegative sigma-finite measure spaces coupled with a proper functional P 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.

The Cheeger problem in abstract measure spaces / Franceschi, V.; Pinamonti, A.; Saracco, G.; Stefani, G.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 109:(2024), pp. e12840.1-e12840.55. [10.1112/jlms.12840]

The Cheeger problem in abstract measure spaces

Saracco, G.
;
2024

Abstract

We consider nonnegative sigma-finite measure spaces coupled with a proper functional P 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.
2024
109
1
55
Franceschi, V.; Pinamonti, A.; Saracco, G.; Stefani, G.
File in questo prodotto:
File Dimensione Formato  
2024 - The Cheeger problem in abstract measure spaces - Franceschi, Pinamonti, Saracco, Stefani.pdf

accesso aperto

Tipologia: Pdf editoriale (Version of record)
Licenza: Open Access
Dimensione 478.12 kB
Formato Adobe PDF
478.12 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1347363
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact