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Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets

Carmen Calvo-JuradoJuan Casado-DíazManuel Luna-Laynez — 2009

ESAIM: Control, Optimisation and Calculus of Variations


For a fixed bounded open set Ω N , a sequence of open sets Ω n Ω and a sequence of sets Γ n Ω Ω n , we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ω n , satisfying Neumann boundary conditions on Γ n and Dirichlet boundary conditions on  Ω n Γ n . We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on Ω n and Γ n locally.


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