On vibrations of bodies with concentrated masses near boundaries (Q812309)

The author discusses a spectral problem for elliptic equation which describes composites with nonperiodic inclusions in the half--space. The sizes and masses of inclusions are proportional to \(\varepsilon\) and to \(\varepsilon^{-m}\) (\(m>2\)), respectively. It is proved that the eigenvalues \(\lambda_{\varepsilon}^k\) of the stated problem and \(\Lambda_0^k\) of the homogenized problem (\(\varepsilon \to 0\)) satisfy the estimate \(| \varepsilon^{2-m} \lambda_{\varepsilon}^k - \Lambda_0^k| \leq C_k \varepsilon^{m-2}\).