Geodesic
Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 49-67

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For a fixed bounded open set Ω⊂ℝ 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.

DOI : 10.1051/cocv:2008021
Classification : 35B40
Keywords: homogenization, varying domains, nonlinear problems 
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     author = {Calvo-Jurado, Carmen and Casado-D{\'\i}az, Juan and Luna-Laynez, Manuel},
     title = {Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {49--67},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {1},
     year = {2009},
     doi = {10.1051/cocv:2008021},
     mrnumber = {2488568},
     zbl = {1170.35014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008021/}
}
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Calvo-Jurado, Carmen; Casado-Díaz, Juan; Luna-Laynez, Manuel. Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 49-67. doi: 10.1051/cocv:2008021

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