Solutions to nonlinear elliptic equations with a nonlocal boundary condition.
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some estimates concerning the Zeeman effect
The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.
Some Estimations of Positive and Negative Eigenvalues for an Inhomogeneous Membrane
Some logarithmic function spaces, entropy numbers, applications to spectral theory [Book]
Some new problems in spectral optimization
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Some properties of Legendre functions and related applications.
Some remarks on a result of Talenti
Some remarks on the number of solutions of some nonlinear elliptic problems
Some topics in spectral geometry
Spectral approximation of variationally formulated eigenvalue problems on curved domains.
Spectral Estimates for Magnetic Operators.
Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.
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...