On Correctors for Spectral Problems in the Homogenization of Robin Boundary Conditions with Very Large Parameters

We obtain estimates for convergence rates of the eigenelements (λε, uε) 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(εα). Here we consider the most significant case where α = κ = 2. AMS Subject Classification: 35B27, 35B40, 35P05, 35P15