Homogenization in general periodically perforated domains by a spectral approach (Q1849399)

The author considers the classical Neumann problem in an \(\varepsilon\)-periodically perforated bounded set, showing that the homogenization process depends on the asymptotic behaviour of the spectrum of the local problem. He studies the case when there exists an eigenvalue \(\Lambda_n(\varepsilon)\) of the above mentioned spectrum such that \(\Lambda_n(\varepsilon)\gg \varepsilon^2\), proving that if \(n\) is the smallest integer with this property, then the homogenized system is a linear system of \(n\) second-order equations.