Elliptische Differentialgleichungen mit variablen Koeffizienten in Gebieten mit unbeschränktem Rand.
Entropy and localization of eigenfunctions
Équation de Schrödinger en dimension 2, avec potentiel et champ magnétique périodiques. Cas d'un réseau triangulaire de puits
Équation de transport. Théorie spectrale et approximation de la diffusion
Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales
Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs de type Fokker-Planck géométrique agissant sur le fibré cotangent d’une variété riemannienne compacte . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.
Équations de Schrödinger avec potentiels singuliers et à longue portée dans l'approximation de liaison forte
Équations des ondes amorties
Équirépartition de fonctions propres pour des problèmes aux limites
Errata - De l'exposé n° XVII de B. Helffer et de J. Sjöstrand «Analyse semi-classique pour l'équation de Harper»
Erratum : “Analytic properties of the resolvent for the Helmholtz operator oustide a periodic surface”
Erratum of “The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent”
Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Error estimate in the generalized Szegö theorem
Error estimates for the Coupled Cluster method
The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Essential Selfadjointness of Dirac Operators with a Strongly Singular Potential.
Essential self-adjointness of symmetric linear relations associated to first order systems
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...
Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field
Estimates for second order derivatives of eigenvectors in thin anisotropic plates with variable thickness.
Estimates for the Asymptotic Behavior of Solutions of the Helmholtz Equation, with an Application to Second order Elliptic Differential Operators with Variable Coefficients.