Regularity results for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position

Abstract

We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an ellipsoidal density that is Hölder continuous with respect to the position variable.