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.

For a fixed bounded open set Ω N , a sequence of open sets Ω n Ω and a sequence of sets Γ n ΩΩ 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 : https://doi.org/10.1051/cocv:2008021
Classification : 35B40
Mots clés : homogenization, varying domains, nonlinear problems
@article{COCV_2009__15_1_49_0,
     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},
     zbl = {1170.35014},
     mrnumber = {2488568},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2009__15_1_49_0/}
}
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. http://www.numdam.org/item/COCV_2009__15_1_49_0/

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