Reiterated Homogenization of Linear Eigenvalue Problems in Multiscale Perforated Domains Beyond the Periodic Setting

Abstract

Reiterated homogenization of linear elliptic Neuman eigenvalue problems in multiscale perforated domains is considered beyond the periodic setting. The classical periodicity hypothesis on the coefficients of the operator is here substituted on each microscale by an abstract hypothesis covering a large set of concrete behaviors such as the periodicity, the almost periodicity, the weakly almost periodicity and many more besides. Furthermore, the usual double periodicity is generalized by considering a type of structure where the perforations on each scale follow not only the periodic distribution but also more complicated but realistic ones. Our main tool is Nguetseng's Sigma convergence.