Singular Limits in Free Boundary Problems

Abstract

We analyze the following class of nonlinear eigenvalue problems: find (uµ) є B x R satisfying (1) Du + µH(a.u - 1)f(u) = 0 in Ω ⊆ R^N, (2) u = O on ∂Ω. Here H (X) is the Heaviside step-function defined by H(X) =0, X ≤ 0 H (X) = 1 X > 0. B is some Banach space appropriate to the problem. D is taken to be a (possibly nonlinear) differential operator with the property than, when µ = 0, equations (1,2) have the unique solution