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Society for Industrial and Applied Mathematics, SIAM Journal on Mathematical Analysis, 5(44), p. 3186-3216

DOI: 10.1137/110835190

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From Poincaré to Logarithmic Sobolev Inequalities: A Gradient Flow Approach

Journal article published in 2012 by Jean Dolbeault ORCID, Bruno Nazaret, Giuseppe Savaré
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This paper is available in a repository.

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Abstract

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.