  We study almost-minimizers of anisotropic surface energies defined by a
H\"older 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 H\"older 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.

Analysis of PDEs