The optimal evolution of the free energy of interacting gases and its applications

DOI10.1016/S1631-073X(03)00289-9zbMath1095.49012MaRDI QIDQ1428306

Xiaosong Kang, Martial Agueh, Nassif Ghoussoub

Publication date: 25 March 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

energy functionalFisher informationYoung functionHWBI inequalitiesHWI inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods applied to PDEs (35A15) Variational problems in a geometric measure-theoretic setting (49Q20) Degenerate parabolic equations (35K65) Methods involving semicontinuity and convergence; relaxation (49J45) Probabilistic potential theory (60J45) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (1)

Contractions in the 2-Wasserstein length space and thermalization of granular media

Cites Work

• Unnamed Item
• A convexity principle for interacting gases
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• Geometric inequalities via a general comparison principle for interacting gases
• Geometric asymptotics and the logarithmic Sobolev inequality

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