Asymptotics of the spectrum of inhomogeneous plate with light-weight stiff inclusions

The Dirichlet spectral problem for an elliptic operator of the fourth order with singularly perturbed coefficients is considered. The problem describes the eigenmodes of a plate with finite number of the stiff and light-weight inclusions of an arbitrary shape. The asymptotic behavior of eigenvalues and eigenfunctions is studied. The number-by-number convergence of the eigenvalues and the corresponding eigenspaces is established. The limit eigenvalue problem involves a non-local boundary conditions. Justification of the asymptotic formulas is based on the norm resolvent convergence of a family of unbounded self-adjoint operators.