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Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales

Gilles Lebeau (2007)

Annales de l’institut Fourier

Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs P de type Fokker-Planck géométrique agissant sur le fibré cotangent Σ = T * X d’une variété riemannienne compacte X . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour P , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.

Error estimates for the Coupled Cluster method

Thorsten Rohwedder, Reinhold Schneider (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

Mikhail Shubin (1998/1999)

Séminaire Équations aux dérivées partielles

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 self-adjointness of symmetric linear relations associated to first order systems

Matthias Lesch (2000)

Journées équations aux dérivées partielles

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...

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