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The Wulff Problem For Diffuse Interface
We consider the non local free energy functional defined in "Bellettini, G., De Masi, A. and E. Presutti: Energy levels of critical points of a nonlocal" and we study its $\inf$ over the class of functions with zero average (Wulff problem). We prove that the $\inf$ 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.