We consider a generalization of the Cheeger problem in a bounded, open set Ω by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable powers of a weighted volume. We show that any connected minimizer A of this weighted Cheeger problem such that H^{n-1}(A^{(1)}∩ ∂A) = 0 satisfies a relative isoperimetric inequality. If Ω itself is a connected minimizer such that H^{n-1}(Ω^{(1)}∩ ∂Ω) = 0, then it allows the classical Sobolev and BV embeddings and the classical BV trace theorem. The same result holds for any connected minimizer whenever the weights grant the regularity of perimeter-minimizer sets and Ω is such that | ∂Ω | = 0 and H^{n-1}(Ω^{(1)}∩ ∂Ω) = 0.

Weighted Cheeger sets are domains of isoperimetry / Saracco, G.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 156:3-4(2018), pp. 371-381. [10.1007/s00229-017-0974-z]

Weighted Cheeger sets are domains of isoperimetry

Saracco G.
2018-01-01

Abstract

We consider a generalization of the Cheeger problem in a bounded, open set Ω by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable powers of a weighted volume. We show that any connected minimizer A of this weighted Cheeger problem such that H^{n-1}(A^{(1)}∩ ∂A) = 0 satisfies a relative isoperimetric inequality. If Ω itself is a connected minimizer such that H^{n-1}(Ω^{(1)}∩ ∂Ω) = 0, then it allows the classical Sobolev and BV embeddings and the classical BV trace theorem. The same result holds for any connected minimizer whenever the weights grant the regularity of perimeter-minimizer sets and Ω is such that | ∂Ω | = 0 and H^{n-1}(Ω^{(1)}∩ ∂Ω) = 0.
2018
3-4
Saracco, G.
Weighted Cheeger sets are domains of isoperimetry / Saracco, G.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 156:3-4(2018), pp. 371-381. [10.1007/s00229-017-0974-z]
File in questo prodotto:
File Dimensione Formato  
2018 - Weighted Cheeger sets are domains of isoperimetry - Saracco.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 442.55 kB
Formato Adobe PDF
442.55 kB Adobe PDF   Visualizza/Apri

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

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/314315
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 14
social impact