C. Villani

发表

Optimal Transport: Old and New

C. Villani, 2008 .

Topics in Optimal Transportation

C. Villani, 2003 .

Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

C. Villani, F. Otto, 2000 .

A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit

Maria G. Westdickenberg, C. Villani, F. Otto, 2009 .

Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media

C. Villani, R. McCann, J. Carrillo, 2006 .

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

C. Villani, R. McCann, J. Carrillo, 2003 .

Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities

C. Villani, F. Bolley, 2005 .

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

C. Villani, A. Guillin, F. Bolley, 2005, math/0503123.

Optimal Transportation and Applications

C. Villani, G. Buttazzo, L. Ambrosio, 2003 .

ON THE TREND TO EQUILIBRIUM FOR THE FOKKER-PLANCK EQUATION : AN INTERPLAY BETWEEN PHYSICS AND FUNCTIONAL ANALYSIS

C. Villani, P. Markowich, 2004 .

The founding fathers of optimal transport

C. Villani, 2009 .

Entropy Production and Convergence to Equilibrium

C. Villani, 2008 .

Ricci curvature for metric-measure spaces via optimal transport

C. Villani, J. Lott, 2004, math/0412127.

Chapter 2C – H Theorem and Trend to Equilibrium

C. Villani, 2002 .

Chapter 2E – Open Problems and New Trends

C. Villani, 2002 .

On Landau damping

C. Villani, C. Mouhot, 2009, 0904.2760.

Birth of a Theorem: A Mathematical Adventure

Cédric Villani, C. Villani, M. Debevoise, 2015 .

A MASS-TRANSPORTATION APPROACH TO SHARP SOBOLEV AND GAGLIARDO-NIRENBERG INEQUALITIES

C. Villani, Bruno Nazaret, D. Cordero-Erausquin, 2004 .

Regularity of optimal transport in curved geometry: The nonfocal case

C. Villani, G. Loeper, 2010 .

Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory

C. Villani, 2002 .

On the trend to global equilibrium in spatially inhomogeneous entropy‐dissipating systems: The linear Fokker‐Planck equation

C. Villani, L. Desvillettes, 2001 .

Regularity of optimal transport andcut locus: From nonsmooth analysis to geometry to smooth analysis

Cédric Villani, C. Villani, 2011 .

Hamilton–Jacobi semigroup on length spaces and applications

John Lott, C. Villani, J. Lott, 2006 .

On Landau damping

Cl'ement Mouhot, C. Villani, C. Mouhot, 2009, 0904.2760.

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

C. Villani, V. Panferov, I. Gamba, 2007 .

On the Boltzmann Equation for Diffusively Excited Granular Media

Irene M. Gamba, C. Villani, V. Panferov, 2004 .

On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations

Cédric Villani, C. Villani, 1998 .

On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness

Cédric Villani, Laurent Desvillettes, C. Villani, 2000 .

Cercignani's Conjecture is Sometimes True and Always Almost True

Cédric Villani, C. Villani, 2003 .

On the Boltzmann equation for long‐range interactions

Radjesvarane Alexandre, Cédric Villani, C. Villani, 2002 .

Entropy Dissipation and Long-Range Interactions

Radjesvarane Alexandre, Bernt Wennberg, Cédric Villani, 2000 .

On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications

Cédric Villani, Laurent Desvillettes, C. Villani, 2000 .

On the Trend to Equilibrium for Some Dissipative Systems with Slowly Increasing a Priori Bounds

Giuseppe Toscani, Cédric Villani, C. Villani, 2000 .

On the Landau approximation in plasma physics

Radjesvarane Alexandre, Cédric Villani, C. Villani, 2004 .

Synthetic theory of Ricci curvature bounds

C. Villani, 2015 .

Optimal transportation, dissipative PDE’s and functional inequalities

Cédric Villani, C. Villani, 2003 .

Ir)reversibility and Entropy

C. Villani, 2012 .

Mathematisches Forschungsinstitut Oberwolfach Report No . 54 / 2010 DOI : 10 . 4171 / OWR / 2010 / 54 Classical and Quantum Mechanical Models of Many-Particle Systems

C. Villani, E. Carlen, 2011 .

Geometry of optimal transportation

C. Villani, 2003 .

Optimal Transportation: Preface

Yann Ollivier, Hervé Pajot, Cédric Villani, 2014 .

Optimal Transportation: SHORT COURSES

Yann Ollivier, Hervé Pajot, Cédric Villani, 2014 .

Sharp Entropy Dissipation Bounds and Explicit Rate of Trend to Equilibrium for the Spatially Homogeneous Boltzmann Equation

Giuseppe Toscani, Cédric Villani, C. Villani, 1999 .

On the Origins of Mathematics

C. Villani, P. Cartier, J. Dhombres, 2016 .

Displacement interpolation and displacement convexity

C. Villani, 2003 .

Ricci curvature for metric-measure spaces via optimal transport

C. Villani, J. Lott, 2004, math/0412127.

Hamilton–Jacobi semigroup on length spaces and applications

C. Villani, J. Lott, 2006, math/0612560.

Synthetic theory of Ricci curvature bounds

C. Villani, 2016, Japanese Journal of Mathematics.

Freedom in Mathematics

Cédric Villani, Pierre Cartier, Gerhard Heinzmann, 2016 .

Weak curvature conditions and functional inequalities

C. Villani, J. Lott, 2005, math/0506481.

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

C. Villani, V. Panferov, I. Gamba, 2007, math/0701081.

On the Boltzmann Equation for Diffusively Excited Granular Media

C. Villani, V. Panferov, I. Gamba, 2003, math/0302348.

Nearly Round Spheres Look Convex

C. Villani, A. Figalli, L. Rifford, 2012 .

Tangent cut loci on surfaces

Cédric Villani, Ludovic Rifford, Alessio Figalli, 2011 .

On the Cauchy problem for Landau equation: sequential stability, global existence

Cédric Villani, C. Villani, 1996, Advances in Differential Equations.

On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation

Cédric Villani, Laurent Desvillettes, C. Villani, 2005 .

ON THE SPATIALLY HOMOGENEOUS LANDAU EQUATION FOR MAXWELLIAN MOLECULES

Cédric Villani, C. Villani, 1998 .

Celebrating Cercignani's conjecture for the Boltzmann equation

C. Villani, C. Mouhot, L. Desvillettes, 2010, 1009.4006.

Gradient flows I

Cédric Villani, C. Villani, 2009 .

Lyapunov functionals for boundary-driven nonlinear drift–diffusion equations

C. Villani, J. Lebowitz, C. Mouhot, 2013, 1305.7405.

John Forbes Nash Jr. (1928–2015)

Camillo De Lellis, C. Villani, J. Milnor, 2016 .

Particle systems and nonlinear Landau dampinga)

C. Villani, 2014 .

Mathematics of Granular Materials

Cédric Villani, C. Villani, 2006 .

On a variant of Korn's inequality arising in statistical mechanics

C. Villani, L. Desvillettes, 2002 .

NECESSARY AND SUFFICIENT CONDITIONS FOR CONTINUITY OF OPTIMAL TRANSPORT MAPS ON RIEMANNIAN MANIFOLDS

Cédric Villani, Ludovic Rifford, Alessio Figalli, 2011 .

On the Ma–Trudinger–Wang curvature on surfaces

Cédric Villani, Ludovic Rifford, Alessio Figalli, 2010 .

On the Landau approximation in plasma physics Sur l’approximation de Landau en physique des plasmas

C. Villani, R. Alexandrea, 2004 .

ENTROPY DISSIPATION AND LONG-RANGE INTERACTIONSR

C. Villani, L. Desvillettes, B. Wennberg, 2000 .

Landau damping Cédric Villani

C. Villani, 2010 .

Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010

C. Villani, 2010 .

The Wasserstein distances

Cédric Villani, C. Villani, 2009 .

Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit

Lorenzo Pareschi, Giuseppe Toscani, Cédric Villani, 2010, Numerische Mathematik.

Donner un sens à l'intelligence artificielle

Marc Schoenauer, Cédric Villani, Bertrand Rondepierre, 2018 .

Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research

Ansgar Jüngel, Giuseppe Toscani, Cédric Villani, 2004 .

Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

C. Villani, E. Caglioti, 2002 .

Probability Metrics and Uniqueness of the Solution to the Boltzmann Equation for a Maxwell Gas

Giuseppe Toscani, Cédric Villani, C. Villani, 1999 .

Optimal Transport: Old and New

C. Villani, 2008 .

Optimal Transport and Curvature

Cédric Villani, Alessio Figalli, C. Villani, 2011 .

Hypocoercivity

C. Villani, Hypocoercivity Cédric Villani, C. Villani, 2006, math/0609050.

PARTICLE SYSTEMS AND NONLINEAR LANDAU DAMPING

C. Villani, 2013 .

Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation wi

C. Villani, 1999 .

Local Aronson–Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

C. Villani, P. Lu, Lei Ni, 2008, 0806.1142.

Convergence to Equilibrium: Entropy Production and Hypocoercivity

C. Villani, 2005 .

Fisher information estimates for Boltzmann's collision operator

Cédric Villani, C. Villani, 1998 .

Regularity Theory for the Spatially Homogeneous Boltzmann Equation with Cut-Off

Cl'ement Mouhot, C. Villani, C. Mouhot, 2004, math/0607539.

On the Inelastic Boltzmann Equation with Diffusive Forcing

C. Villani, V. Panferov, I. Gamba, 2002 .

Nonlinear PDE’s and Applications

C. Villani, E. Carlen, A. Mielke, 2011 .

53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 49Q15 Geometric measure and integration theory, integral and normal currents in optimization

C. Villani, Karl-Theodor Sturm, J. Lott, 2022 .

Comment on: “Hypercontractivity of Hamilton–Jacobi equations”, by S. Bobkov, I. Gentil and M. Ledoux

C. Villani, F. Otto, 2001 .

Entropy and chaos in the Kac model

C. Villani, M. C. Carvalho, M. Loss, 2008, 0808.3192.

The kinetic Fokker – Planck equation

C. Villani, 2008 .

Hypocoercive Diffusion Operators

Cédric Villani, C. Villani, 2006 .

Conservative forms of Boltzmann's collision operator: Landau revisited

Cédric Villani, C. Villani, 1999 .

H-theorem and beyond: Boltzmann's entropy in today's mathematics

Cédric Villani, C. Villani, 2008 .

A short proof of the "Concavity of entropy power"

Cédric Villani, C. Villani, 2000, IEEE Trans. Inf. Theory.

On The Trend To Global Equilibrium In Spatially Inhomogeneous Entropy-Dissipating Systems Part I : T

Cédric Villani, Laurent Desvillettes, C. Villani, 1999 .

STABILITY OF A 4TH-ORDER CURVATURE CONDITION ARISING IN OPTIMAL TRANSPORT THEORY

C. Villani, 2008 .

ENTROPIC METHODS FOR THE STUDY OF THE LONG TIME BEHAVIOR OF KINETIC EQUATIONS

C. Villani, L. Desvillettes, 2001 .

ON THE TREND TO EQUILIBRIUM FOR SOLUTIONS OF THE BOLTZMANN EQUATION : QUANTITATIVE VERSIONS OF BOLTZMANN

C. Villani, 2007 .

ENTROPIC METHODS FOR THE STUDYOF THE LONG TIME BEHAVIOR OF KINETIC EQUATIONSL

C. Villani, 2000 .

A Curved Brunn-Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?

Yann Ollivier, Cédric Villani, C. Villani, 2010, SIAM J. Discret. Math..

ENTROPY AND CHAOS IN THE KAC MODEL Dedicated to Professor Giuseppe Toscani on the occasion of his sixtieth birthday

Jonathan Le Roux, C. Villani, E. Carlen, 2009 .

Stability of optimal transport

Cédric Villani, C. Villani, 2009 .