Γ-Asymptotic developments, the Cahn-Hilliard functional, and curvatures

Abstract

Given a smooth, bounded open set Ω ⊂ Rn and a positive smooth function g: ∂Ω → R, we consider the numbers (formula presented) and we obtain the asymptotic formula mε = εC1(g) + ε2C2(g) + ο(ε2), where (formula presented) K1 being the mean curvature of ∂Ω. This is related to phase transition problems. Asymptotic developments by Γ-convergence are used. © 1996 Academic Press, Inc.