Homogenization of eigenvalue problems of elasticity in perforated domains

Abstract

In this paper, we study the homogenization of eigenvalue problem associated with the elasticity system in a periodically (with period ε>0, a small parameter) perforated domain with tiny holes. The critical size of the holes a_ε is given by a_ε=C₀ε^N/N−2 if N≥3 and a_ε=exp (−C₀/ε²) if N=2, where C₀ is a constant and N is the dimension. We will study the above eigenvalue problem as ε→0 and eigenvalues and eigenvectors.