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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
6/2007

The Wulff Problem For Diffuse Interface

Guido Manzi

Abstract

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.

Received:
Jan 23, 2007
Published:
Jan 23, 2007
MSC Codes:
74A50, 82C24
Keywords:
diffuse interface, tunneling

Related publications

inJournal
2007 Repository Open Access
Guido Manzi

The Wulff problem for diffuse interfaces

In: Zeitschrift fuer Analysis und ihre Anwendungen, 26 (2007) 3, pp. 261-275