Nonlinear reinforcement problems with right-hand side in L1

We study the asymptotic behaviour, as ε goes to zero, of the entropy solution uε to a class of nonlinear elliptic problems whose prototype is −div ( (δε)p−1 |∇uε|p−2∇uε ) = f ε in Ωε , uε = 0 on ∂Ωε, where 1 < p < N , Ωε = Ω ∪ Σε, Ω ⊂ R is a bounded domain of class C1,1, surrounded along its boundary by a layer Σε of small thickness ε, δε = 1 in Ω, δε = ε in Σε, and f ε belongs to L1(Ωε). The solutions uε also satisfies natural transmission conditions on ∂Ω.