Convex Sobolev inequalities derived from entropy dissipation

DOI10.1007/s00205-010-0331-9zbMath1229.35302OpenAlexW2061983822MaRDI QIDQ717439

Daniel Matthes, Giuseppe Toscani, Ansgar Jüngel

Publication date: 4 October 2011

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-010-0331-9

zbMATH Keywords

Fokker-Planck equationSobolev inequalityBakry-Émery methodentropy-dissipation relation

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fokker-Planck equations (35Q84)

Related Items (9)

The Poisson equation and estimates for distances between stationary distributions of diffusions ⋮ Structure preserving schemes for Fokker-Planck equations with nonconstant diffusion matrices ⋮ Derivation of wealth distributions from biased exchange of money ⋮ Fokker–Planck equations in the modeling of socio-economic phenomena ⋮ Lipschitz continuity of probability kernels in the optimal transport framework ⋮ Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution ⋮ On a Fokker-Planck equation for wealth distribution ⋮ A non-local problem for the Fokker-Planck equation related to the Becker-Döring model ⋮ Structure preserving stochastic Galerkin methods for Fokker-Planck equations with background interactions

Uses Software

• YALMIP

Cites Work

• Unnamed Item
• Unnamed Item
• Convex Sobolev inequalities and spectral gap
• Self-similarity and power-like tails in nonconservative kinetic models
• Modified logarithmic Sobolev inequalities in discrete settings
• Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
• Hardy-Poincaré inequalities and applications to nonlinear diffusions
• Analysis of a model for wealth redistribution
• On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
• Phi-entropy inequalities for diffusion semigroups
• Asymptotics of the fast diffusion equation via entropy estimates
• Hypercontractivity and the Bakry-Emery criterion for compact Lie groups
• Geometric theory of semilinear parabolic equations
• On an integral criterion for hypercontractivity of diffusion semigroups and extremal functions
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Levels of concentration between exponential and Gaussian
• Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
• Kinetic approach to long time behavior of linearized fast diffusion equations
• \(L^q\)-functional inequalities and weighted porous media equations
• Refined convex Sobolev inequalities
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• Weak logarithmic Sobolev inequalities and entropic convergence
• Two singular diffusion problems
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• A Theory of the Term Structure of Interest Rates
• Poincaré inequalities for linearizations of very fast diffusion equations
• An algorithmic construction of entropies in higher-order nonlinear PDEs
• The Derrida–Lebowitz–Speer–Spohn Equation: Existence, NonUniqueness, and Decay Rates of the Solutions
• A Generalized Poincare Inequality for Gaussian Measures
• Sobolev inequalities for probability measures on the real line
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
• Hardy's inequality with weights

This page was built for publication: Convex Sobolev inequalities derived from entropy dissipation