Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. De Rosa - F. Ghiraldin

Existence results for minimizers of parametric elliptic functionals

created by derosa on 25 Apr 2017
modified on 11 Jan 2022


Published Paper

Inserted: 25 apr 2017
Last Updated: 11 jan 2022

Journal: J. Geom. Anal.
Year: 2020

ArXiv: 1704.07801 PDF


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 \cite{DelGhiMag,DePDeRGhi,DeLDeRGhi16}. 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 by the authors in \cite{DePDeRGhi2}. As a consequence we provide a new proof of Reifenberg existence theorem.