JournalszaaVol. 26 , No. 3DOI 10.4171/zaa/1323

The Wulff Problem for Diffuse Interfaces

  • Guido Manzi

    Università di Roma, Italy
The Wulff Problem for Diffuse Interfaces cover

Abstract

We consider the non-local free energy functional defined by Bellettini, De~Masi and Presutti in [{\it 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.