Existence Results for Minimizers of Parametric Elliptic Functionals

Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1450-1465
Number of pages16
JournalJournal of Geometric Analysis
Issue number2
StatePublished - Apr 1 2020


  • Elliptic integrand
  • Plateau problem
  • Wand varifolds

ASJC Scopus subject areas

  • Geometry and Topology


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