From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach
Savaré, Giuseppe; Nazaret, Bruno; Dolbeault, Jean (2012), From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach, SIAM Journal on Mathematical Analysis, 44, 5, p. 3186-3216. http://dx.doi.org/10.1137/110835190
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00595042/fr/Date
2012Journal name
SIAM Journal on Mathematical AnalysisVolume
44Number
5Publisher
SIAM
Pages
3186-3216
Publication identifier
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Show full item recordAbstract (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.Subjects / Keywords
Kolmogorov-Fokker-Planck equation; Gradient flows; Action functional; Continuity equation; Generalized Poincaré inequality; Kantorovich-Rubinstein-Wasserstein distance; Optimal transportRelated items
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