Regularity results for the variable-coefficient Plateau problem

Abstract

We study almost-minimizers of anisotropic surface energies defined by a Holder continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers are locally Holder continuously differentiable at regular points and give dimension estimates for the size of the singular set . We work in the framework of sets of locally finite perimeter and our proof follows an excess-decay type argument.