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From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00595042/fr/
Dewey
Analyse
Sujet
Kolmogorov-Fokker-Planck equation; Gradient flows; Action functional; Continuity equation; Generalized Poincaré inequality; Kantorovich-Rubinstein-Wasserstein distance; Optimal transport
Journal issue
SIAM Journal on Mathematical Analysis
Volume
44
Number
5
Publication date
2012
Article pages
3186-3216
Publisher
SIAM
DOI
http://dx.doi.org/10.1137/110835190
URI
https://basepub.dauphine.fr/handle/123456789/6336
Collections
  • CEREMADE : Publications
Metadata
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Author
Savaré, Giuseppe
Nazaret, Bruno
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (EN)
We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy with the entropy production functional reflect the contraction properties of the flow. Our approach provides a unified framework for the study of the Kolmogorov-Fokker-Planck (KFP) equation.

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