From Poincar\'e to logarithmic Sobolev inequalities: a gradient flow approach
Analysis of PDEs
2012-12-06 v1
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.
Cite
@article{arxiv.1105.4511,
title = {From Poincar\'e to logarithmic Sobolev inequalities: a gradient flow approach},
author = {Jean Dolbeault and Bruno Nazaret and Giuseppe Savaré},
journal= {arXiv preprint arXiv:1105.4511},
year = {2012}
}