Geometry of anisotropic double crystals

Abstract

An anisotropic double crystal (double crystal in short) is a mathematical model of a simplest multi-crystal. It consists of two connected regions in the space enclosing two prescribed volumes that contact each other. Its energy is the integral of an energy density over the surface, and the energy density depends on the normal direction of the surface at each point. A double crystal is a critical point of this energy. We derive a geometric characterization of double crystals. In a plane, for a certain energy density function, we classify the double crystals in terms of symmetry and the given areas.