The Wulff Problem for Diffuse Interfaces

Abstract

We consider the non-local free energy functional defined by Bellettini, De Masi and Presutti in [J. Math. Phys. 46 (2004)(8)], and we study its infimum over the class of functions with zero average (Wulff problem). We prove that the infimum is a minimum achieved on a particular antisymmetric strictly increasing function called the finite volume instanton. The result can be interpreted as an extension of the Wulff theorem to a not sharp interface.