Affiliations: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy. E-mail: [email protected] | Centre de Mathématiques et Leurs Applications, 61 Avenue du Président Wilson, 94235 Cachan cedex, France. E-mail: [email protected] | Mathématiques, Université d'Orléans, Rue de Chartres, 45067 Orléans cedex 2, France. E-mail: [email protected]
Note: [] Corresponding author.
Abstract: 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)=fε in Ωε, uε=0 on ∂Ωε, where 1<p<N, $\varOmega^{\varepsilon}=\overline{\varOmega}\cup\Sigma^{\varepsilon}$, Ω⊂RN 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 fε belongs to L1(Ωε). The solutions uε also satisfies natural transmission conditions on ∂Ω.
