We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.

Existence Results for Minimizers of Parametric Elliptic Functionals / De Philippis, Guido; De Rosa, Antonio; Ghiraldin, Francesco. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 30(2020), pp. 1450-1465. [10.1007/s12220-019-00165-8]

Existence Results for Minimizers of Parametric Elliptic Functionals

De Philippis, Guido;
2020

Abstract

We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.
30
1450
1465
https://link.springer.com/article/10.1007/s12220-019-00165-8#Sec2
De Philippis, Guido; De Rosa, Antonio; Ghiraldin, Francesco
File in questo prodotto:
File Dimensione Formato  
2019_Existence Results For Minimizers of Parametric Elliptic Functionals.pdf

non disponibili

Descrizione: Pdf articolo
Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 367.05 kB
Formato Adobe PDF
367.05 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/20.500.11767/88001
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 7
social impact