Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene Djellout; Liming Wu

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 2, page 450-465
  • ISSN: 0246-0203

Abstract

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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 examples.

How to cite

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Djellout, Hacene, and Wu, Liming. "Lipschitzian norm estimate of one-dimensional Poisson equations and applications." Annales de l'I.H.P. Probabilités et statistiques 47.2 (2011): 450-465. <http://eudml.org/doc/239783>.

@article{Djellout2011,
abstract = {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 examples.},
author = {Djellout, Hacene, Wu, Liming},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Poisson equations; transportation–information inequalities; concentration and isoperimetric inequalities; transportation-information inequalities},
language = {eng},
number = {2},
pages = {450-465},
publisher = {Gauthier-Villars},
title = {Lipschitzian norm estimate of one-dimensional Poisson equations and applications},
url = {http://eudml.org/doc/239783},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Djellout, Hacene
AU - Wu, Liming
TI - Lipschitzian norm estimate of one-dimensional Poisson equations and applications
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 2
SP - 450
EP - 465
AB - 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 examples.
LA - eng
KW - Poisson equations; transportation–information inequalities; concentration and isoperimetric inequalities; transportation-information inequalities
UR - http://eudml.org/doc/239783
ER -

References

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