Non-periodic boundary homogenization and "light" concentrated masses

We consider certain spectral problems for the Laplace operator with rapidly alternating boundary conditions in an open bounded domain Omega of R-n that contains many concentrated masses B, near the boundary. The regions B-epsilon have a diameter O (epsilon) and the density takes the value epsilon(-m) in B-epsilon and 1 outside. m, n and epsilon are parameters: 0 <= m < 2, n >= 3 and epsilon -> 0. We assume small mass of the whole concentrated masses while periodicity of the microstructure is not assumed. We study the asymptotic behavior, as epsilon -> 0, of the eigenelements of the spectral problems. We obtain the homogenized (limit) spectral problems and estimates for the convergence rates of the corresponding eigenelements. Certain associated stationary problems are also considered, and estimates for the convergence rates of the solutions are obtained.