Spectral properties of even order derivative operators.
Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions
We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface is bounded by the -norm of the magnetic field . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with even in case of the trivial bundle.
Spectral study of a self-adjoint operator on related with a Poincaré type constant
Spectre conforme et métriques extrémales
Spectre négatif d'un opérateur elliptique avec des conditions au bord de Robin.
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
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
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
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.
Spectrum of the weighted Laplace operator in unbounded domains
We investigate the spectral properties of the differential operator , 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 , we study the structure of the spectrum with respect to the parameter . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.
Spherical Symmetrization and Eigenvalue Estimates.
Stability and approximations of eigenvalues and eigenfunctions for the Neumann Laplacian. I.
Stability and semiclassics in self-generated fields
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy 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 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
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
We consider the Neumann Laplacian with constant magnetic field on a regular domain in . Let be the strength of the magnetic field and let be the first eigenvalue of this Laplacian. It is proved that is monotone increasing for large . 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
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
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
Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante.
Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique
Dans cette article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.