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Article type: Research Article
Authors: De Arcangelis, Riccardo | Vitolo, Antonio
Affiliations: Departimento di Ingegneria dell'Informazione e Matematica Applicata, Facoltà di Ingegneria, Università di Salerno, 84084 Fisciano (Salerno), Italy
Abstract: For every bounded open set Ω with Lipschitz boundary, β in L∞(Ω) we study the asymptotic behaviour (as h→∞) of the sequence ih(Ω,β)=inf {∫Ωf(hx,Du)+∫Ωβu, u Lipschitz continuous, u=0 on ∂Ω,|Du(x)|≤ϕ(hx) for a.e. x in Ω} where f is a nonnegative function on Rn×Rn measurable and ]0,1[n-periodic in the x variable, convex in the z variable, ϕ is a ]0,1[n-periodic function from Rn into [0,+∞] such that there exist Θ∈[0,½[, m>0 with 0<m≤ϕ(x) for a.e. x in ]0,1[n−]½−Θ, ½+Θ[n, and one of the following conditions hold: f|z|p≤f(x,z), p>n; or ϕ∈Lp(]0,1[n) p>n. It is proved that ih(Ω,β) converges to a minimim problem of integral type for which an explicit formula is proved.
DOI: 10.3233/ASY-1992-5502
Journal: Asymptotic Analysis, vol. 5, no. 5, pp. 397-428, 1992
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