The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids
type: Item
instance of: scholarly article
title: The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids
zbMATH Open document ID: 1307.35100
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-04-22T00:00:00Z
review text: This paper is devoted to the spectral analysis of the Laplace operator in a periodic waveguide. the waveguide consists in a straight tubular domain of \(\mathbb{R}^d\) containing periodically distributed inclusions. The Laplace operator is defined by means of Dirichlet boundary conditions at the boundary of the guide. It is proved that the essential spectrum of Laplace operator contains open spectral gaps when the diameter of the inclusion is small enough. Furthermore the author gives a precise discussion on the link between the behavior of the spectral band near the band edges and the opening of the corresponding spectral gap. The method employed is based on the asymptotic perturbation theory of linear operators These results are illustrated by some examples.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 6156253
author: Sergei A. Nazarov
reviewed by: Philippe Briet
MaRDI profile type: Publication
full work available at URL: s10958-012-0985-y
OpenAlex ID: W2033697517
cites work: Q3861944
cites work: Isoperimetric Inequalities in Mathematical Physics. (AM-27)
cites work: Floquet theory for partial differential equations
cites work: The mathematics of photonic crystals
cites work: Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains
cites work: Q3683032
cites work: ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES
cites work: Singularities of solutions of the Neumann problem at a conical point
cites work: Opening of a gap in the continuous spectrum of a periodically perturbed waveguide
cites work: A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface
cites work: A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide
cites work: On occurrence of spectral edges for periodic operators inside the Brillouin zone
cites work: On the location of spectral edges in \mathbb {Z}-periodic media
cites work: Gap opening and split band edges in waveguides coupled by a periodic system of small windows
cites work: ABSOLUTE CONTINUITY IN PERIODIC WAVEGUIDES
cites work: Q4436158
cites work: The Schrödinger operator in a periodic waveguide on a plane and quasiconformal mappings
cites work: Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder
cites work: Q5526485
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
cites work: Q4096019
cites work: Q3259838
cites work: Asymptotics of eigenvalues of a plate with small clamped zone
cites work: Mathematical Modelling of Solids with Nonregular Boundaries
DOI: 10.1007/S10958-012-0985-Y
description: scientific article; zbMATH DE number 6156253