Variational models for phase separation

  • Margherita Solci

    Università di Pavia, Italy
  • Enrico Vitali

    Università di Pavia, Italy

Abstract

The paper deals with the asymptotic behaviour (as ) of a family of integral functionals in the framework of phase separation. In order to obtain a selection criterion for the minima of the usual double-well, non-convex free energy involving the phase-variable we add a gradient term in a new variable which is related to through the -distance between and weighted by a coefficient We prove that the limit as is a minimal area model with a surface tension of non-local form. The well-known Modica--Mortola constant can be recovered in this setting as a limit case when

Cite this article

Margherita Solci, Enrico Vitali, Variational models for phase separation. Interfaces Free Bound. 5 (2003), no. 1, pp. 27–46

DOI 10.4171/IFB/70