Lipschitzian Norm Estimate of One-Dimensional Poisson Equations - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2010

Lipschitzian Norm Estimate of One-Dimensional Poisson Equations

Résumé

By direct calculus we identify explicitly the Lipschitzian norm of the solution of the Poisson equation $-\LL G=g$ in terms of various norms of $g$, where $\LL$ 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 $L^1$-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 examples.
Fichier non déposé

Dates et versions

hal-00469834 , version 1 (02-04-2010)

Identifiants

  • HAL Id : hal-00469834 , version 1

Citer

Hacène Djellout, Liming Wu. Lipschitzian Norm Estimate of One-Dimensional Poisson Equations. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2010, accepté pour publication en 2010, 16 p. ⟨hal-00469834⟩
58 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More