
Journal of Convex Analysis 10 (2003), No. 1, 001034 Copyright Heldermann Verlag 2003 Degenerate Perturbations of a TwoPhase Transition Model Roberto Monti Dip. di Matematica, Università die Trento, Via Sommariva 14, 38050 Povo, Italy, rmonti@science.unitn.it Francesco Serra Cassano Dip. di Matematica, Università die Trento, Via Sommariva 14, 38050 Povo, Italy, cassano@science.unitn.it [Abstractpdf] We study the Gconvergence as e approaches 0^{+} of the family of degenerate functionals Q_{e}(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 R^{n}) 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 Glimit functional exploiting some tools of analysis in CarnotCaratheodory spaces. We extend some previous results obtained for the non degenerate perturbations Q_{e} in the classical gradient theory of phase transitions. Keywords: Phase transitions, Γconvergence, CarnotCaratheodory spaces, minimal interface criterion. MSC 2000: 49J45, 49Q05, 49Q20. FullTextpdf (760 K) 