SINGULAR PERTURBATIONS OF VARIATIONAL-PROBLEMS ARISING FROM A 2-PHASE TRANSITION MODEL

Given that α, β are two Lipschitz continuous functions of Ω to ℝ+ and that f(x, u, p) is a continuous function of {Mathematical expression} × ℝ × ℝN to [0, + ∞[ such that, for every x, f(x,·, 0) reaches its minimum value 0 at exactly two points α(x) and β(x), we prove the convergence of Fε(u) = (1/ε)∫Ωf (x, u, εDu) dx when the perturbation parameter ε goes to zero. A formula is given for the limit functional and a general minimal interface criterium is deduced for a wide class of two-phase transition models. Earlier results of [19], [21], and [22] are extended with new proofs. © 1990 Springer-Verlag New York Inc.