Andrii Khrabustovskyi

Periodic elliptic operators with asymptotically preassigned spectrum

We deal with operators in

Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps

mathbb{R}^n

Opening up and control of spectral gaps of the Laplacian in periodic domains

of the form

Asymptotic behaviour of spectrum of Laplace–Beltrami operator on Riemannian manifolds with complex microstructure

mathbf{A}=-{1over mathbf{b}(x)}sumlimits_{k=1}^nds{partialoverpartial x_k}(mathbf{a}(x){partial overpartial x_k})

On the spectrum of narrow Neumann waveguide with periodically distributed

where

\delta \prime

mathbf{a}(x),mathbf{b}(x)

traps

are positive, bounded and periodic functions. We denote by

Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane

mathbf{L}_{mathrm{per}}