IJAM, Volume 26, No. 3 (2013)

Abstract. We obtain estimates for convergence rates of the eigenelements (λ^ε, u^ε) for the Laplace operator in a domain Ω⊂ R³ periodically perforated along a plane γ=Ω∩ {x₁=0}. The boundary conditions are of the Dirichlet type on ∂ Ω and of the Robin type, involving a large parameter O(ε^-κ), on the boundary of the cavities. The small parameter ε denotes the period while the size of each cavity is O(ε^α). Here we consider the most significant case where α=κ=2.