Geodesic
Degenerate Perturbations of a Two-Phase Transition Model
Journal of convex analysis, Tome 10 (2003) no. 1, pp. 001-034.

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We study the G-convergence as e approaches 0+ of the family of degenerate functionals Qe(u) = e Integral over W of <ADu, Du> dx + (1/e) Integral over W of W (u) dx, where A(x) is a symmetric, non negative n times n matrix on W (i.e. <A(x) ξ, ξ> ≥   0 for all x in W and x in Rn) with regular entries and W: R to [0, +infinity) is a double well potential having two isolated minimum points. Moreover, under suitable assumptions on the matrix A, we obtain a minimal interface criterion for the G-limit functional exploiting some tools of analysis in Carnot-Caratheodory spaces. We extend some previous results obtained for the non degenerate perturbations Qe in the classical gradient theory of phase transitions.
Mots-clés : Phase transitions, Γ-convergence, Carnot-Caratheodory spaces, minimal interface criterion 
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     title = {Degenerate {Perturbations} of a {Two-Phase} {Transition} {Model}},
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R. Monti; F. Serra Cassano. Degenerate Perturbations of a Two-Phase Transition Model. Journal of convex analysis, Tome 10 (2003) no. 1, pp. 001-034. http://geodesic.mathdoc.fr/item/JCA_2003_10_1_JCA_2003_10_1_a0/