Homogenization of elliptic equations with singular perturbations in perforated domains (Q6614242)

The paper under review deals with the homogenization of elliptic equations with singular perturbations in perforated domains. More precisely, the authors obtain quantitative and qualitative results for the homogenization of the elliptic system\N\[\N\left \{ \begin{array}{ll} \epsilon^\alpha \Delta^2 u_\epsilon -\Delta u_\epsilon =f & \text{in } \Omega^\epsilon,\\\Nu_\epsilon =\frac{\partial u_\epsilon}{\partial n}=0 & \text{on } \partial \Omega^\epsilon, \end{array} \right.\N\]\Nwhere \(\alpha >0\), \(n\) is the outward unit normal to the boundary, \(\Omega^\epsilon\) a periodically perforated domain with periodic holes of size \(\epsilon\), and \(\epsilon\) a positive small parameter.