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arXiv · 1105.4511

From Poincar\'e to logarithmic Sobolev inequalities: a gradient flow approach

Jean Dolbeault·Bruno Nazaret·Giuseppe Savaré
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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.

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Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré. 2011-05-23. From Poincar\'e to logarithmic Sobolev inequalities: a gradient flow approach. https://arxiv.org/abs/1105.4511

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