Geodesic
A property of the \(H\)-convergence for elasticity in perforated domains
Electronic journal of differential equations, Tome 2006 (2006)
In this article, we obtain the $H_{e}^{0}$-convergence as a limit case of the $H_{e}$-convergence. More precisely, if $\Omega_{\varepsilon}$ is a perforated domain with (admissible) holes $T_{\varepsilon}$ and $\chi_{\varepsilon}$ denote its characteristic function and if $(A^{\varepsilon},T_{\varepsilon}) \rightharpoonup A^{0}$, we show how the behavior as $(\varepsilon,\delta)\to(0,0)$ of the double sequence of tensors $A^{\varepsilon}_{\delta}=(\chi_{\varepsilon} +\delta(1-\chi_{\varepsilon})) A^{\varepsilon}$ is connected to $A^{0}$. These results extend those given by Cioranescu, Damlamian, Donato and Mascarenhas in [3] for the $H$-convergence of the scalar second elliptic operators to the linearized elasticity systems.
Classification : 35B40, 74B05
Keywords: homogenization, H-convergence, linearized elasticity system, perforated domains 
@article{EJDE_2006__2006__a8,
     author = {Haddadou,  Hamid},
     title = {A property of the {\(H\)-convergence} for elasticity in perforated domains},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1128.35017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a8/}
}
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Haddadou,  Hamid. A property of the \(H\)-convergence for elasticity in perforated domains. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a8/