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Spectral estimates of vibration frequencies of anisotropic beams

Luca Sabatini (2023)

Applications of Mathematics

The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.

Spectral properties of even order derivative operators.

Sadallah, Boubaker-Khaled (2003)

Applied Mathematics E-Notes [electronic only]

Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions

László Erdős (2002)

Annales de l’institut Fourier

We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface $M$ is bounded by the $L^{1}$ -norm of the magnetic field $B$ . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with $\int_{M} | B |$ even in case of the trivial bundle.

Spectral study of a self-adjoint operator on $L^{2} (Ω)$ related with a Poincaré type constant

Maurice Gaultier, Mikel Lezaun (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Spectre conforme et métriques extrémales

Bruno Colbois (2003/2004)

Séminaire de théorie spectrale et géométrie

Spectre négatif d'un opérateur elliptique avec des conditions au bord de Robin.

Yuri V. Egorov, Mohammed El Aidi (2001)

Publicacions Matemàtiques

In this article we discuss some estimates of the number of the negative eigenvalues and their moments of energy for an elliptic operator L = L0 - V(x) defined in Hm(R+n) with the Robin boundary conditions containing a potential W(x), in terms of some integrals of V and W.

Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...

Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...

Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2014)

Mathematica Bohemica

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...

Spectrum of the linearized operator for the Ginzburg-Landau equation.

Lin, Tai-Chia (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

We investigate the spectral properties of the differential operator $- r^{s} Δ$ , $s \geq 0$ with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm ${∥ u ∥}_{L_{2, s} (Ω)}^{2} = \int_{Ω} r^{- s} {| u |}^{2} d x$ , we study the structure of the spectrum with respect to the parameter $s$ . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.

Spherical Symmetrization and Eigenvalue Estimates.

Emanuel, Jr. Sperner (1981)

Mathematische Zeitschrift

Stability and approximations of eigenvalues and eigenfunctions for the Neumann Laplacian. I.

Bañuelos, Rodrigo, Pang, Michael M.H. (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Stability and semiclassics in self-generated fields

László Erdős, Soren Fournais, Jan Philip Solovej (2013)

Journal of the European Mathematical Society

We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$ . The total energy includes the field energy $β \int B^{2}$ and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter $β$ tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...

Stabilization of Schrödinger equation in exterior domains

Lassaad Aloui, Moez Khenissi (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.

Strong diamagnetism for general domains and application

Soeren Fournais, Bernard Helffer (2007)

Annales de l’institut Fourier

We consider the Neumann Laplacian with constant magnetic field on a regular domain in $ℝ^{2}$ . Let $B$ be the strength of the magnetic field and let $λ_{1} (B)$ be the first eigenvalue of this Laplacian. It is proved that $B \mapsto λ_{1} (B)$ is monotone increasing for large $B$ . Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

Study of some noncooperative linear elliptic systems

Ali Djellit, Saadia Tas (2004)

Applications of Mathematics

Using an approximation method, we show the existence of solutions for some noncooperative elliptic systems defined on an unbounded domain.

Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method

Pengzhan Huang (2014)

Applications of Mathematics

This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.

Sur des estimations des valeurs propres d'opérateurs elliptiques

Yuri V. Egorov (1991/1992)

Séminaire Équations aux dérivées partielles (Polytechnique)

Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante.

B., Colin de Verdière de Colbois (1988)

Commentarii mathematici Helvetici

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