Asymptotics for eigenvalues of the Laplacian in higher dimensional periodically perforated domains

摘要: This paper considers the periodic spectral problem associated with Laplace operator written in \({\mathbb{R}^N}\) (N = 3, 4, 5) periodically perforated by balls, and homogeneous Dirichlet condition on boundary of holes. We give an asymptotic expansion for all simple eigenvalues as size holes goes to zero. As application this result, we use Bloch waves find classical strange term homogenization theory, zero faster than microstructure period.