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Zeitschrift für Analysis und ihre Anwendungen

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Volume 26, Issue 3, 2007, pp. 261–275
DOI: 10.4171/ZAA/1323

Published online: 2007-09-30

The Wulff Problem for Diffuse Interfaces

Guido Manzi[1]

(1) Università di Roma, Italy

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.

Keywords: Diffuse interface, tunneling

Manzi Guido: The Wulff Problem for Diffuse Interfaces. Z. Anal. Anwend. 26 (2007), 261-275. doi: 10.4171/ZAA/1323