We investigate two linear conductivity problems, with strongly contrasting conductivity, in a
thin heterogeneous cylinder with a small cross-section of radius hn, n in N. In this cylinder …

We turn back to the well known problem of interpretation of the Schrodinger operator with
the pseudopotential being the first derivative of the Dirac function. We show that the problem …

We consider an asymptotic spectral problem for a second order differential operator, with
piecewise constants coefficients, in a two-dimensional domain Ωɛ. Here Ωɛ is Ωɛ= Ω∪ …

We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin
structure Ω ε, where ε denotes the transversal thickness of both branches. We assume the …

We study the localization effect for the eigenfunctions of the Laplace-Dirichlet problem in a
thin three-dimensional plate with curved non-smooth bases. We show that the …

In this paper we consider the multiscale analysis of a Steklov eigenvalue equation with
rapidly oscillating coefficients arising from the modeling of a composite media with a …

We study the asymptotic behavior of the eigenvalues $\beta^\varepsilon $ and the
associated eigenfunctions of an $\varepsilon $-dependent Steklov type eigenvalue problem …

We investigate a degenerating elliptic problem in a multi-structure" of R 3, in the framework
of the thermal stationary conduction with highly contrasting diffusivity. Precisely," consists of …

We consider a two-dimensional spectral problem of Steklov type for the Laplace operator in
a domain divided into two parts by a perforated partition with a periodic microstructure. The …

Усреднение спектральных задач в областях с микроструктурой–важная и во многих
случаях трудная проблема. Первые результаты в этом направлении были получены в …