On eigenvibrations of a body with “light” concentrated masses on the surface
María‐Eugenia Pérez‐Martínez, Gregory Aleksandrovich Chechkin, Ekaterina Ivanovna Yablokova · Russian Mathematical Surveys · 2002
Statement of the problem. We consider a spectral problem for the Laplace operator with a rapidly varying type of boundary conditions in a domain with a large number of concentrated masses near the boundary. Without assuming periodicity of the microstructure of the domain the authors treat the case when the density of the concentrated masses is not large. Similar problems are considered in [1] and [2] for domains with concentrated masses located periodically along the boundary. In [3] the problem is studied with an arbitrary structure of the distribution of the boundary conditions in domains with constant density. Let Ω ⊂ R n be a bounded domain with smooth boundary, n 3. We assume that ∂ Ω= Γe∪γe, with Γe = N e k=1 Γ k e , where diam(Γ k e ) 2e, and the distance between two of the sets Γ k e is at least 2e; e is a small positive parameter.