Existence Results for Minimizers of Parametric Elliptic Functionals

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.