Displaying similar documents to “A non elliptic spectral problem related to the analysis of superconducting micro-strip lines”

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators A n , n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

Localization effects for eigenfunctions near to the edge of a thin domain

Serguei A. Nazarov (2002)

Mathematica Bohemica

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It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ω h is localized either at the whole lateral surface Γ h of the domain, or at a point of Γ h , while the eigenfunction decays exponentially inside Ω h . Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.

Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain....

Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

Journées équations aux dérivées partielles

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After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator H . If H is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in (, 24:759–775, 1999) and obtain a lower bound which leads to a generalization of Thirring’s inequality...