On the spectrum of the Laplace operator on the infinite Dirichlet ladder

DOI10.1090/S1061-0022-2012-01228-8zbMath1273.35195OpenAlexW1989199361MaRDI QIDQ2849082

Sergueï A. Nazarov

Publication date: 16 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2012-01228-8

zbMATH Keywords

Dirichlet problemessential spectrumdiscrete spectrumgapsperiodic junction of thin domains

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (6)

Existence of guided waves due to a lineic perturbation of a 3D periodic medium ⋮ Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder ⋮ Asymptotics of eigenvalues in spectral gaps under regular perturbations of walls of a periodic waveguide ⋮ Spectral gaps in a thin-walled infinite rectangular Dirichlet box with a periodic family of cross walls ⋮ Structure of the spectrum of a net of quantum waveguides and bounded solutions of a model problem at the threshold ⋮ Open waveguides in a thin Dirichlet ladder. I: Asymptotic structure of the spectrum

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