Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension -
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In the junction $\Omega $ of several semi-infinite cylindrical waveguides, the Dirichlet
Laplacian is treated whose continuous spectrum is the ray $[\lambda _\dagger,+\infty) $ with …

The spectral properties of the restricted fractional Dirichlet Laplacian in ${\sf V} $-shaped
waveguides are studied. The continuous spectrum for such domains with cylindrical outlets …

The structure of the spectrum of the three-dimensional Dirichlet Laplacian in the 3D
polyhedral layer of fixed width is studied. It appears that the essential spectrum is defined by …

В работе проводится анализ структуры спектра оператора Лапласа с условиями
Дирихле на границе в слоях постоянной толщины, построенным по многогранным …

The asymptotics of eigenvalues and eigenfunctions of the Dirichlet problem for the
biharmonic operator in a narrow two-dimensional domain (a thin Kirchhoff plate with rigidly …

The spectrum of truncated cross-shaped waveguides is studied under the Dirichlet
conditions on the lateral surface and various boundary conditions on the ends of the column …

Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the
Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped …

1.1. Мотивировка. Краевые задачи Дирихле (D) и Неймана (N) для оператора Лапласа
в тонких областях, статические (st) и спектральные (sp), изучены в достаточной …