La première valeur propre du laplacien pour le problème de Dirichlet
La structure de la matrice pour le problème à trois corps
Landesman–Lazer type conditions and quasilinear elliptic equations
Large atoms in large magnetic fields
L'asymptotique de Weyl pour les bouteilles magnétiques
Le comportement de la résolvante modifiée du laplacien pour des obstacles captifs
Le papillon de Hofstadter revisité
L'equazione . Teoremi di completezza
In ipotesi molto generali si dimostrano teoremi di completezza nel senso di Picone per l'equazione (1). Come corollario si ottengono teoremi del tipo Runge.
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Lieb–Thirring inequalities with improved constants
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb–Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrödinger operators.
Liens entre les résonances pour l'opérateur de Dirac et de Schrödinger
Limit on the excess negative charge of a dynamic diatomic molecule
Limite semi-classique de l'amplitude de diffusion
Limiting absorption principle for the Dirac operator
Lipschitzian norm estimate of one-dimensional Poisson equations and applications
By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...
Ljusternik-Schnirelmann theory on -manifolds
Local decay estimates for Schrödinger operators with long range potentials
Local Decay in time of solutions to Schrödinger's equation with a dilation-analytic interaction.
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Local Exchange Potentials for Electronic Structure Calculations
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...