Geodesic
Variational models for phase separation
Margherita Solci1 ; Enrico Vitali1
1Università di Pavia, Italy
Interfaces and free boundaries, Tome 5 (2003) no. 1, pp. 27-46

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DOI

The paper deals with the asymptotic behaviour (as ε→0) of a family Fε​(u,v) 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 u, we add a gradient term in a new variable v which is related to u through the L2-distance between u and v, weighted by a coefficient α. We prove that the limit as ε→0 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 α→+∞.
DOI : 10.4171/ifb/70
Classification : 01-XX, 00-XX
Mots-clés : Phase separation; non-local models; variational methods; Γ-convergence

Margherita Solci  1   ; Enrico Vitali  1

1 Università di Pavia, Italy 
Margherita Solci; Enrico Vitali. Variational models for phase separation. Interfaces and free boundaries, Tome 5 (2003) no. 1, pp. 27-46. doi: 10.4171/ifb/70
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