The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices

DOI10.1134/S0037446613030166zbMath1307.35178OpenAlexW1978115598MaRDI QIDQ359380

Sergueï A. Nazarov

Publication date: 12 August 2013

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446613030166

zbMATH Keywords

Dirichlet problemspectral gapslocalization of eigenfunctionsasymptotics of spectrum

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (10)

Discrete spectrum of cranked quantum and elastic waveguides ⋮ Asymptotics of eigenvalues of the Dirichlet problem in a skewed ℐ-shaped waveguide ⋮ Two-dimensional asymptotic models of thin cylindrical elastic gaskets ⋮ Eigenmodes of a thin elastic layer between periodic rigid profiles ⋮ Localization of eigenfunctions in the Dirichlet beaker ⋮ Remark on justification of asymptotics of spectra of cylindrical waveguides with periodic singular perturbations of boundary and coefficients ⋮ Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube ⋮ Asymptotics of the natural oscillations of a thin elastic gasket between absolutely rigid profiles ⋮ Localization effect for Dirichlet eigenfunctions in thin non-smooth domains ⋮ Localization of eigenfunctions in a narrow Kirchhoff plate

Cites Work

• Unnamed Item
• On the spectrum of the Dirichlet Laplacian in a narrow strip
• Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
• On the spectrum of narrow periodic waveguides
• Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\)
• Existence theorems for trapped modes
• Localization effects for eigenfunctions near to the edge of a thin domain
• The Localization Effect for Eigenfunctions of the Mixed Boundary Value Problem in a Thin Cylinder with Distorted Ends
• Floquet theory for partial differential equations

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