The Wulff problem for diffuse interfaces (Q2460705)

Summary: We consider the nonlocal free energy functional defined by \textit{G. Bellettini} et al. [J. Math. Phys. 46, No. 8, 1--31 (2005)], 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 ot the Wulff theorem to a non-sharp interface.