2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142198Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed. Two-scale limit equations are derived and relate to certain non-standard self-adjoint operators. In particular they explicitly display the first two terms in the asymptotic expansion for the eigenvalues, with a surprising bound for the error of order ε^{5/4} proved.23 pages, 2 figuresSpectral TheoryAnalysis of PDEs35B27; 34Etext