Logarithmic Sobolev inequalities for some nonlinear PDE's

By Florent Malrieu. 2001

169 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/305fa8d0bfd820376e72b4fc3591026cce730a77

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2017, methodology): “as in the classical result [68]; see also [3,11,20,67] for more on the classical Lipschitz case.”
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates (2003, background): “This theorem improves in several respects on [4] (in which L(1) convergence was proven for the particular case of the cubic potential in dimension 1, without any rate) and on Malrieu [22] who was the first to prove exponential trend to equilibrium in L(1) sense for equations of the same type, althou”
Mean Field Limit for Stochastic Particle Systems (2017, background): “The results referred to here were mostly obtained in [9, 10, 13, 57, 58].”
Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, methodology): “We then employ a well known relative entropy estimate for diffusions related to Girsanov’s theorem, used in many prior studies [50, 34, 36, 37, 49] to estimate the global quantity H(P (n,n) t |μ t ) but apparently not the local quantities Hk t := H(P (n,k) t |μ t ).”
Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming (2010, methodology): “For space-homogeneous kinetic models it was extended to non-Lipschitz drifts by means of convexity arguments, first in one dimension in [4], then more generally in any dimension in [13, 27].”
Probabilistic approach for granular media equations in the non-uniformly convex case (2006, methodology): “Under the strong assumptions of (global) uniform convexity of one of the potentials (the other one being globally convex but non necessarily uniformly), Malrieu [ 14 ,15] successively fulfilled these two goals using extensively the so called Bakry-Emery criterion ensuring that a Logarithmic Sobolev ”
On Kac's chaos and related problems (2012, background): “There exists at least one more way to guaranty chaoticity which is very popular because that chaos formulation naturally appears in the probabilistic coupling technique, see [61], as well as [43, 12, 11] and the references therein.”