# Existence results for minimizers of parametric elliptic functionals

## TL;DR

This paper establishes a compactness principle for anisotropic minimal sets in the Plateau problem, providing new proofs of rectifiability and existence theorems in geometric measure theory.

## Contribution

It introduces a novel strategy for proving rectifiability of minimal sets using an anisotropic version of Allard's theorem, leading to new existence results.

## Key findings

- Proved a compactness principle for anisotropic minimal sets.
- Developed a new approach for rectifiability based on anisotropic Allard's theorem.
- Provided a new proof of Reifenberg's existence theorem.

## 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 \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.