Singular perturbation problems with a compact support semilinear term

Abstract

In this paper we study the asymptotic behaviour of the functionals

F_ε(u)=∫_Ω[ε|∇u|²+ε⁻³β(u/ε)]dx

where β is a non-negative lower semicontinuous function with compact support. When ε tends to 0, the limit functional corresponds to a least area problem with an obstacle.