The Łojasiewicz inequality for free energy functionals on a graph

DOI10.3934/cpaa.2022066zbMath1506.35240OpenAlexW4226184418MaRDI QIDQ2087545

Kongzhi Li, Xiao-Ping Xue

Publication date: 21 October 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2022066

zbMATH Keywords

Fokker-Planck equationŁojasiewicz inequalitysimple graphoptimal transportTalagrand inequality

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Rate of convergence, degree of approximation (41A25) Optimality conditions for free problems in two or more independent variables (49K10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Fokker-Planck equations (35Q84) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Entropy dissipation of Fokker-Planck equations on graphs
• A discrete Schrödinger equation via optimal transport on graphs
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
• Fokker-Planck equations for a free energy functional or Markov process on a graph
• Entropy dissipation semi-discretization schemes for Fokker-Planck equations
• Lower bounds of the Laplacian graph eigenvalues
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Singular Perturbation Methods in Stochastic Differential Equations of Mathematical Physics
• The Variational Formulation of the Fokker--Planck Equation
• Geodesics of minimal length in the set of probability measures on graphs
• On the Łojasiewicz exponent of Kuramoto model
• The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems

This page was built for publication: The Łojasiewicz inequality for free energy functionals on a graph