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Author ID: villani.cedric Recent zbMATH articles by "Villani, Cédric"
Published as: Villani, Cédric; Villani, C.; Villani, Cedric
Homepage: http://cedricvillani.org
External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Awards: EMS Prize (2008) · Fields Medal (2010)
all top 5

Co-Authors

46 single-authored
10 Desvillettes, Laurent
7 Figalli, Alessio
6 Mouhot, Clément
5 Toscani, Giuseppe
4 Rifford, Ludovic
3 Alexandre, Radjesvarane
3 Carrillo de la Plata, José Antonio
3 Martínez Gamba, Irene
3 Lott, John
3 Otto, Felix
3 Panferov, Vladislav A.
2 Bolley, François
2 Carlen, Eric Anders
2 Cartier, Pierre
2 Dhombres, Jean G.
2 Heinzmann, Gerhard
2 Maggi, Francesco
2 Markowich, Peter Alexander
2 McCann, Robert J.
2 Ollivier, Yann
2 Uzan, Jean-Philippe
1 Ambrosio, Luigi
1 Arnold, Anton
1 Banyaga, Augustin
1 Baudoin, Edmond
1 Bodineau, Thierry
1 Brenier, Yann
1 Brydges, David C.
1 Buss, Samuel R.
1 Busser, Elisabeth
1 Buttazzo, Giuseppe
1 Caffarelli, Luis Ángel
1 Caglioti, Emanuele
1 Carvalho, Maria Conceição
1 Cederbaum, Carla
1 Comtet, Alain
1 Cordero-Erausquin, Dario
1 De Lellis, Camillo
1 Dickenstein, Alicia M.
1 Dolbeault, Jean
1 Faris, William G.
1 Gangbo, Wilfrid
1 Golse, François
1 Gondard, Claude
1 Greuel, Gert-Martin
1 Gross, Leonhard
1 Grünberg, David
1 Grunewald, Natalie
1 Guillin, Arnaud
1 Hauchecorne, Bertrand
1 Hook, Julian L.
1
1 Jackson, Allyn
1 Jüngel, Ansgar
1 King, Henry C.
1 Lawler, Gregory Francis
1 Le Roux, Jonathan
1 Lebowitz, Joel Louis
1 Lederman, Claudia B.
1 Lions, Pierre-Louis
1 Loeper, Grégoire
1 Loss, Michael
1 Lu, Peng
1 Luca, Florian
1 Milnor, John Willard
1 Moncorgé, Vincent
1 Nachbar, John H.
1 Nazaret, Bruno
1 Nelson, Joseph Edward
1 Neudauer, Nancy Ann
1 Ni, Lei
1 Nordlinger, Bernard
1 Olla, Stefano
1 Pajot, Hervé
1 Pareschi, Lorenzo
1 Park, Hyungju
1 Rezakhanlou, Fraydoun
1 Salsa, Sandro
1 Shubin, Carol Ann
1 Simon, Barry
1 Székelyhidi, László jun.
1 Valiant, Leslie Gabriel
1 Vazquez, Juan Luis
1 Waldschmidt, Michel
1 Weinstein, Jonathan
1 Wennberg, Bernt
1 Westdickenberg, Maria G.
all top 5

Serials

6 Archive for Rational Mechanics and Analysis
4 Journal of Statistical Physics
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Communications in Mathematical Physics
3 Journal of Functional Analysis
2 Communications on Pure and Applied Mathematics
2 Acta Mathematica
2 Revista Matemática Iberoamericana
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
2 Communications in Partial Differential Equations
2 Notices of the American Mathematical Society
2 Calculus of Variations and Partial Differential Equations
2 European Mathematical Society Newsletter
2 Lecture Notes in Mathematics
2 Kinetic and Related Models
1 IEEE Transactions on Information Theory
1 Journal of Mathematical Physics
1 Nonlinearity
1 Transport Theory and Statistical Physics
1 Advances in Mathematics
1 American Journal of Mathematics
1 Duke Mathematical Journal
1 Gazette des Mathématiciens
1 Inventiones Mathematicae
1 Mathematische Zeitschrift
1 Memoirs of the American Mathematical Society
1 Monatshefte für Mathematik
1 Numerische Mathematik
1 Tôhoku Mathematical Journal. Second Series
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Probability Theory and Related Fields
1 SIAM Journal on Discrete Mathematics
1 Differential Geometry and its Applications
1 The Journal of Geometric Analysis
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Séminaire Équations aux Dérivées Partielles
1 Journal of the Egyptian Mathematical Society
1 Methods and Applications of Analysis
1 Advances in Differential Equations
1 Discrete and Continuous Dynamical Systems
1 Matemática Contemporânea
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Markov Processes and Related Fields
1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica
1 Annals of Mathematics. Second Series
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Graduate Studies in Mathematics
1 Grundlehren der Mathematischen Wissenschaften
1 London Mathematical Society Lecture Note Series
1 Mathematical Notes (Princeton)
1 Japanese Journal of Mathematics. 3rd Series
1 Matapli
1 La Tortue de Zénon

Publications by Year

Citations contained in zbMATH Open

87 Publications have been cited 6,718 times in 4,145 Documents Cited by Year
Topics in optimal transportation. Zbl 1106.90001
Villani, Cédric
2003
Optimal transport. Old and new. Zbl 1156.53003
Villani, Cédric
2009
Ricci curvature for metric-measure spaces via optimal transport. Zbl 1178.53038
Lott, John; Villani, Cedric
457
2009
A review of mathematical topics in collisional kinetic theory. Zbl 1170.82369
Villani, Cédric
356
2002
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. Zbl 0985.58019
Otto, F.; Villani, C.
309
2000
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Zbl 1073.35127
Carrillo, José A.; McCann, Robert J.; Villani, Cédric
182
2003
On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Zbl 0912.45011
Villani, Cédric
163
1998
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Zbl 1162.82316
Desvillettes, L.; Villani, C.
152
2005
Contractions in the 2-Wasserstein length space and thermalization of granular media. Zbl 1082.76105
Carrillo, José A.; McCann, Robert J.; Villani, Cédric
150
2006
A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Zbl 1048.26010
Cordero-Erausquin, D.; Nazaret, B.; Villani, C.
134
2004
On Landau damping. Zbl 1239.82017
Mouhot, Clément; Villani, Cédric
126
2011
Hypocoercivity. Zbl 1197.35004
Villani, Cédric
124
2009
Entropy dissipation and long-range interactions. Zbl 0968.76076
Alexandre, R.; Desvillettes, L.; Villani, C.; Wennberg, B.
122
2000
On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation. Zbl 1029.82032
Desvillettes, L.; Villani, C.
116
2001
Stability of a 4th-order curvature condition arising in optimal transport theory. Zbl 1158.53036
Villani, C.
110
2008
On the spatially homogeneous Landau equation for hard potentials. I: Existence, uniqueness and smoothness. Zbl 0946.35109
Desvillettes, Laurent; Villani, Cédric
98
2000
On the Boltzmann equation for long-range interactions. Zbl 1029.82036
Alexandre, R.; Villani, C.
77
2002
On the spatially homogeneous Landau equation for hard potentials. II: H-theorem and applications. Zbl 0951.35130
Desvillettes, Laurent; Villani, Cédric
70
2000
Weak curvature conditions and functional inequalities. Zbl 1119.53028
Lott, John; Villani, Cédric
68
2007
Cercignani’s conjecture is sometimes true and always almost true. Zbl 1041.82018
Villani, Cédric
68
2003
Quantitative concentration inequalities for empirical measures on non-compact spaces. Zbl 1113.60093
Bolley, François; Guillin, Arnaud; Villani, Cédric
68
2007
Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. Zbl 0958.82044
Toscani, G.; Villani, C.
66
1999
On the Landau approximation in plasma physics. Zbl 1044.83007
Alexandre, R.; Villani, C.
58
2004
Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Zbl 1063.76086
Mouhot, Clément; Villani, Cédric
56
2004
On the spatially homogeneous Landau equation for Maxwellian molecules. Zbl 0957.82029
Villani, C.
55
1998
Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028
Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric
54
2003
On the Boltzmann equation for diffusively excited granular media. Zbl 1106.82031
Gamba, I. M.; Panferov, V.; Villani, C.
53
2004
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Zbl 1087.60008
Bolley, François; Villani, Cédric
50
2005
On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. Zbl 1139.82326
Markowich, P. A.; Villani, C.
46
2000
Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. Zbl 1156.58015
Lu, Peng; Ni, Lei; Vázquez, Juan-Luis; Villani, Cédric
43
2009
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. Zbl 1273.76373
Gamba, I. M.; Panferov, V.; Villani, C.
41
2009
Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Zbl 0944.35066
Toscani, G.; Villani, C.
40
1999
On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. Zbl 1034.82032
Toscani, G.; Villani, C.
37
2000
Entropy and chaos in the Kac model. Zbl 1186.76675
Carlen, Eric A.; Carvalho, Maria C.; Le Roux, Jonathan; Loss, Michael; Villani, Cédric
37
2010
On the Cauchy problem for Landau equations: Sequential stability, global existence. Zbl 0856.35020
Villani, Cédric
33
1996
Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109
Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C.
31
2004
On a variant of Korn’s inequality arising in statistical mechanics. Zbl 1092.82032
Desvillettes, L.; Villani, Cédric
31
2002
Mathematics of granular materials. Zbl 1134.82040
Villani, Cédric
31
2006
Regularity of optimal transport in curved geometry: the nonfocal case. Zbl 1192.53041
Loeper, Grégoire; Villani, Cédric
30
2010
A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Zbl 1179.60068
Grunewald, Natalie; Otto, Felix; Villani, Cédric; Westdickenberg, Maria G.
28
2009
Nearly round spheres look convex. Zbl 1241.53031
Figalli, Alessio; Rifford, Ludovic; Villani, Cedric
28
2012
Hamilton-Jacobi semigroup on length spaces and applications. Zbl 1210.53047
Lott, John; Villani, Cédric
27
2007
Hypocoercive diffusion operators. Zbl 1130.35027
Villani, Cédric
26
2006
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Zbl 0934.45010
Villani, Cédric
24
1999
A short proof of the “concavity of entropy power”. Zbl 0994.94018
Villani, Cédric
24
2000
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
24
2011
Balls have the worst best Sobolev inequalities. Zbl 1086.46021
Maggi, Francesco; Villani, Cédric
23
2005
On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
22
2010
A curved Brunn-Minkowski inequality on the discrete hypercube, or: what is the Ricci curvature of the discrete hypercube? Zbl 1267.52010
Ollivier, Y.; Villani, C.
20
2012
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Zbl 1106.65324
Pareschi, L.; Toscani, G.; Villani, C.
19
2003
Fisher information estimates for Boltzmann’s collision operator. Zbl 0918.60093
Villani, C.
18
1998
Landau damping. Zbl 1247.82081
Mouhot, Clément; Villani, Cédric
17
2010
Celebrating Cercignani’s conjecture for the Boltzmann equation. Zbl 1217.82064
Desvillettes, Laurent; Mouhot, Clément; Villani, Cédric
15
2011
Balls have the worst best Sobolev inequalities. II: Variants and extensions. Zbl 1135.46016
Maggi, F.; Villani, C.
14
2008
Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Zbl 1301.58017
Bodineau, Thierry; Lebowitz, Joel; Mouhot, Clément; Villani, Cédric
12
2014
Entropy production and convergence to equilibrium. Zbl 1128.76056
Villani, Cédric
11
2008
Optimal regularity for square roots. (Régularité optimale de racines carrées.) Zbl 0870.35017
Lions, Pierre-Louis; Villani, Cédric
10
1995
Conservative forms of Boltzmann’s collision operator: Landau revisited. Zbl 0919.35140
Villani, Cédric
7
1999
Trend to equilibrium for dissipative equations, functional inequalities and mass transportation. Zbl 1134.35375
Villani, Cédric
7
2004
An approximation lemma about the cut locus, with applications in optimal transport theory. Zbl 1172.53022
Figalli, Alessio; Villani, Cédric
7
2008
\(H\)-theorem and beyond: Boltzmann’s entropy in today’s mathematics. Zbl 1156.82313
Villani, Cédric
7
2008
Synthetic theory of Ricci curvature bounds. Zbl 1353.53019
Villani, Cédric
7
2016
Homogeneous cooling states are not always good approximations to granular flows. Zbl 1053.74012
Caglioti, E.; Villani, C.
6
2002
Hydrodynamic limits of Boltzmann’s equation (following C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). (Limites hydrodynamiques de l’équation de Boltzmann (d’après C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond).) Zbl 1119.82037
Villani, Cédric
6
2002
Regularity of optimal transport and cut locus: from nonsmooth analysis to geometry to smooth analysis. Zbl 1225.49048
Villani, Cédric
6
2011
Optimal transportation, dissipative PDE’s and functional inequalities. Zbl 1039.35147
Villani, Cedric
5
2003
Hypocoercive diffusion operators. Zbl 1178.35306
Villani, Cédric
5
2007
Entropic methods for the study of the long time behavior of kinetic equations. Zbl 1038.82073
Desvillettes, L.; Villani, C.
5
2001
Comment on “Hypercontractivity of Hamilton-Jacobi equations” by S. G. Bobkov, I. Gentil and M. Ledoux. Zbl 1134.35312
Otto, Felix; Villani, Cédric
5
2001
Decrease of the Fisher information for solutions of the spatially homogeneous Landau equation with Maxwellian molecules. Zbl 1010.82023
Villani, C.
4
2000
Entropy methods for the Boltzmann equation. Lectures from a special semester at the Centre Émil Borel, Instititut H. Poincaré, Paris 2001. Zbl 1125.76001
Rezakhanlou, Fraydoun; Villani, Cédric
4
2008
The living theorem. (Théorème vivant.) Zbl 1290.01002
Villani, Cédric
4
2012
Diffusion, quantum theory, and radically elementary mathematics. Zbl 1104.81003
4
2006
Tangent cut loci on surfaces. Zbl 1217.53038
Figalli, A.; Rifford, L.; Villani, C.
4
2011
Optimal transport and Ricci curvature. (Transport optimal et courbure de Ricci.) Zbl 1141.53030
Villani, Cédric
3
2006
Entropy production and convergence to equilibrium for the Boltzmann equation. Zbl 1221.82082
Villani, Cédric
3
2005
Optimal transport and curvature. Zbl 1247.53003
Figalli, Alessio; Villani, Cédric
3
2011
Optimal transport. Theory and applications. Proceedings of the summer school ‘Optimal transportation: theory and applications’, Fourier Institute, Grenoble, France. Zbl 1301.00076
2
2014
(Ir)reversibility and entropy. Zbl 1320.82036
Villani, Cédric
2
2013
Landau damping. Zbl 1307.76087
Villani, Cédric
2
2013
Strong displacement convexity on Riemannian manifolds. Zbl 1125.53026
Figalli, A.; Villani, C.
2
2007
Rate of convergence toward the equilibrium in degenerate settings. Zbl 1069.35011
Desvillettes, L.; Villani, C.
1
2004
On the trend to equilibrium for kinetic equations. Zbl 1128.82303
Villani, C.
1
2002
On the inelastic Boltzmann equation with diffusive forcing. Zbl 1032.76065
Gamba, Irene M.; Panferov, Vladislav; Villani, Cedric
1
2002
The Scheffer-Shnirelman paradox revisited from the viewpoint of convex integration (after C. De Lellis and L. Szḱelyhidi). (Paradoxe de Scheffer-Shnirelman revu sous l’angle de l’intégration convexe (d’après C. De Lellis et L. Székelyhidi).) Zbl 1404.35338
Villani, Cédric
1
2010
Optimal transport: Monge meets Riemann and Fourier. Zbl 1246.49041
Villani, Cédric
1
2011
(Ir)reversibility and entropy. Zbl 1259.82089
Villani, Cédric
1
2012
Synthetic theory of Ricci curvature bounds. Zbl 1353.53019
Villani, Cédric
7
2016
Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Zbl 1301.58017
Bodineau, Thierry; Lebowitz, Joel; Mouhot, Clément; Villani, Cédric
12
2014
Optimal transport. Theory and applications. Proceedings of the summer school ‘Optimal transportation: theory and applications’, Fourier Institute, Grenoble, France. Zbl 1301.00076
2
2014
(Ir)reversibility and entropy. Zbl 1320.82036
Villani, Cédric
2
2013
Landau damping. Zbl 1307.76087
Villani, Cédric
2
2013
Nearly round spheres look convex. Zbl 1241.53031
Figalli, Alessio; Rifford, Ludovic; Villani, Cedric
28
2012
A curved Brunn-Minkowski inequality on the discrete hypercube, or: what is the Ricci curvature of the discrete hypercube? Zbl 1267.52010
Ollivier, Y.; Villani, C.
20
2012
The living theorem. (Théorème vivant.) Zbl 1290.01002
Villani, Cédric
4
2012
(Ir)reversibility and entropy. Zbl 1259.82089
Villani, Cédric
1
2012
On Landau damping. Zbl 1239.82017
Mouhot, Clément; Villani, Cédric
126
2011
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
24
2011
Celebrating Cercignani’s conjecture for the Boltzmann equation. Zbl 1217.82064
Desvillettes, Laurent; Mouhot, Clément; Villani, Cédric
15
2011
Regularity of optimal transport and cut locus: from nonsmooth analysis to geometry to smooth analysis. Zbl 1225.49048
Villani, Cédric
6
2011
Tangent cut loci on surfaces. Zbl 1217.53038
Figalli, A.; Rifford, L.; Villani, C.
4
2011
Optimal transport and curvature. Zbl 1247.53003
Figalli, Alessio; Villani, Cédric
3
2011
Optimal transport: Monge meets Riemann and Fourier. Zbl 1246.49041
Villani, Cédric
1
2011
Entropy and chaos in the Kac model. Zbl 1186.76675
Carlen, Eric A.; Carvalho, Maria C.; Le Roux, Jonathan; Loss, Michael; Villani, Cédric
37
2010
Regularity of optimal transport in curved geometry: the nonfocal case. Zbl 1192.53041
Loeper, Grégoire; Villani, Cédric
30
2010
On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
22
2010
Landau damping. Zbl 1247.82081
Mouhot, Clément; Villani, Cédric
17
2010
The Scheffer-Shnirelman paradox revisited from the viewpoint of convex integration (after C. De Lellis and L. Szḱelyhidi). (Paradoxe de Scheffer-Shnirelman revu sous l’angle de l’intégration convexe (d’après C. De Lellis et L. Székelyhidi).) Zbl 1404.35338
Villani, Cédric
1
2010
Optimal transport. Old and new. Zbl 1156.53003
Villani, Cédric
2009
Ricci curvature for metric-measure spaces via optimal transport. Zbl 1178.53038
Lott, John; Villani, Cedric
457
2009
Hypocoercivity. Zbl 1197.35004
Villani, Cédric
124
2009
Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. Zbl 1156.58015
Lu, Peng; Ni, Lei; Vázquez, Juan-Luis; Villani, Cédric
43
2009
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. Zbl 1273.76373
Gamba, I. M.; Panferov, V.; Villani, C.
41
2009
A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Zbl 1179.60068
Grunewald, Natalie; Otto, Felix; Villani, Cédric; Westdickenberg, Maria G.
28
2009
Stability of a 4th-order curvature condition arising in optimal transport theory. Zbl 1158.53036
Villani, C.
110
2008
Balls have the worst best Sobolev inequalities. II: Variants and extensions. Zbl 1135.46016
Maggi, F.; Villani, C.
14
2008
Entropy production and convergence to equilibrium. Zbl 1128.76056
Villani, Cédric
11
2008
An approximation lemma about the cut locus, with applications in optimal transport theory. Zbl 1172.53022
Figalli, Alessio; Villani, Cédric
7
2008
\(H\)-theorem and beyond: Boltzmann’s entropy in today’s mathematics. Zbl 1156.82313
Villani, Cédric
7
2008
Entropy methods for the Boltzmann equation. Lectures from a special semester at the Centre Émil Borel, Instititut H. Poincaré, Paris 2001. Zbl 1125.76001
Rezakhanlou, Fraydoun; Villani, Cédric
4
2008
Weak curvature conditions and functional inequalities. Zbl 1119.53028
Lott, John; Villani, Cédric
68
2007
Quantitative concentration inequalities for empirical measures on non-compact spaces. Zbl 1113.60093
Bolley, François; Guillin, Arnaud; Villani, Cédric
68
2007
Hamilton-Jacobi semigroup on length spaces and applications. Zbl 1210.53047
Lott, John; Villani, Cédric
27
2007
Hypocoercive diffusion operators. Zbl 1178.35306
Villani, Cédric
5
2007
Strong displacement convexity on Riemannian manifolds. Zbl 1125.53026
Figalli, A.; Villani, C.
2
2007
Contractions in the 2-Wasserstein length space and thermalization of granular media. Zbl 1082.76105
Carrillo, José A.; McCann, Robert J.; Villani, Cédric
150
2006
Mathematics of granular materials. Zbl 1134.82040
Villani, Cédric
31
2006
Hypocoercive diffusion operators. Zbl 1130.35027
Villani, Cédric
26
2006
Diffusion, quantum theory, and radically elementary mathematics. Zbl 1104.81003
4
2006
Optimal transport and Ricci curvature. (Transport optimal et courbure de Ricci.) Zbl 1141.53030
Villani, Cédric
3
2006
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Zbl 1162.82316
Desvillettes, L.; Villani, C.
152
2005
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Zbl 1087.60008
Bolley, François; Villani, Cédric
50
2005
Balls have the worst best Sobolev inequalities. Zbl 1086.46021
Maggi, Francesco; Villani, Cédric
23
2005
Entropy production and convergence to equilibrium for the Boltzmann equation. Zbl 1221.82082
Villani, Cédric
3
2005
A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Zbl 1048.26010
Cordero-Erausquin, D.; Nazaret, B.; Villani, C.
134
2004
On the Landau approximation in plasma physics. Zbl 1044.83007
Alexandre, R.; Villani, C.
58
2004
Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Zbl 1063.76086
Mouhot, Clément; Villani, Cédric
56
2004
On the Boltzmann equation for diffusively excited granular media. Zbl 1106.82031
Gamba, I. M.; Panferov, V.; Villani, C.
53
2004
Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109
Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C.
31
2004
Trend to equilibrium for dissipative equations, functional inequalities and mass transportation. Zbl 1134.35375
Villani, Cédric
7
2004
Rate of convergence toward the equilibrium in degenerate settings. Zbl 1069.35011
Desvillettes, L.; Villani, C.
1
2004
Topics in optimal transportation. Zbl 1106.90001
Villani, Cédric
2003
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Zbl 1073.35127
Carrillo, José A.; McCann, Robert J.; Villani, Cédric
182
2003
Cercignani’s conjecture is sometimes true and always almost true. Zbl 1041.82018
Villani, Cédric
68
2003
Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028
Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric
54
2003
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Zbl 1106.65324
Pareschi, L.; Toscani, G.; Villani, C.
19
2003
Optimal transportation, dissipative PDE’s and functional inequalities. Zbl 1039.35147
Villani, Cedric
5
2003
A review of mathematical topics in collisional kinetic theory. Zbl 1170.82369
Villani, Cédric
356
2002
On the Boltzmann equation for long-range interactions. Zbl 1029.82036
Alexandre, R.; Villani, C.
77
2002
On a variant of Korn’s inequality arising in statistical mechanics. Zbl 1092.82032
Desvillettes, L.; Villani, Cédric
31
2002
Homogeneous cooling states are not always good approximations to granular flows. Zbl 1053.74012
Caglioti, E.; Villani, C.
6
2002
Hydrodynamic limits of Boltzmann’s equation (following C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). (Limites hydrodynamiques de l’équation de Boltzmann (d’après C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond).) Zbl 1119.82037
Villani, Cédric
6
2002
On the trend to equilibrium for kinetic equations. Zbl 1128.82303
Villani, C.
1
2002
On the inelastic Boltzmann equation with diffusive forcing. Zbl 1032.76065
Gamba, Irene M.; Panferov, Vladislav; Villani, Cedric
1
2002
On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation. Zbl 1029.82032
Desvillettes, L.; Villani, C.
116
2001
Entropic methods for the study of the long time behavior of kinetic equations. Zbl 1038.82073
Desvillettes, L.; Villani, C.
5
2001
Comment on “Hypercontractivity of Hamilton-Jacobi equations” by S. G. Bobkov, I. Gentil and M. Ledoux. Zbl 1134.35312
Otto, Felix; Villani, Cédric
5
2001
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. Zbl 0985.58019
Otto, F.; Villani, C.
309
2000
Entropy dissipation and long-range interactions. Zbl 0968.76076
Alexandre, R.; Desvillettes, L.; Villani, C.; Wennberg, B.
122
2000
On the spatially homogeneous Landau equation for hard potentials. I: Existence, uniqueness and smoothness. Zbl 0946.35109
Desvillettes, Laurent; Villani, Cédric
98
2000
On the spatially homogeneous Landau equation for hard potentials. II: H-theorem and applications. Zbl 0951.35130
Desvillettes, Laurent; Villani, Cédric
70
2000
On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. Zbl 1139.82326
Markowich, P. A.; Villani, C.
46
2000
On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. Zbl 1034.82032
Toscani, G.; Villani, C.
37
2000
A short proof of the “concavity of entropy power”. Zbl 0994.94018
Villani, Cédric
24
2000
Decrease of the Fisher information for solutions of the spatially homogeneous Landau equation with Maxwellian molecules. Zbl 1010.82023
Villani, C.
4
2000
Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. Zbl 0958.82044
Toscani, G.; Villani, C.
66
1999
Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Zbl 0944.35066
Toscani, G.; Villani, C.
40
1999
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Zbl 0934.45010
Villani, Cédric
24
1999
Conservative forms of Boltzmann’s collision operator: Landau revisited. Zbl 0919.35140
Villani, Cédric
7
1999
On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Zbl 0912.45011
Villani, Cédric
163
1998
On the spatially homogeneous Landau equation for Maxwellian molecules. Zbl 0957.82029
Villani, C.
55
1998
Fisher information estimates for Boltzmann’s collision operator. Zbl 0918.60093
Villani, C.
18
1998
On the Cauchy problem for Landau equations: Sequential stability, global existence. Zbl 0856.35020
Villani, Cédric
33
1996
Optimal regularity for square roots. (Régularité optimale de racines carrées.) Zbl 0870.35017
Lions, Pierre-Louis; Villani, Cédric
10
1995
all top 5

Cited by 3,915 Authors

98 Carrillo de la Plata, José Antonio
42 Toscani, Giuseppe
39 Figalli, Alessio
39 Mouhot, Clément
35 Sturm, Karl-Theodor
35 Villani, Cédric
35 Yang, Tong
34 Ambrosio, Luigi
32 Gigli, Nicola
32 Li, Wuchen
29 Desvillettes, Laurent
29 Savaré, Giuseppe
28 McCann, Robert J.
28 Morimoto, Yoshinori
28 Santambrogio, Filippo
27 Carlier, Guillaume
26 Dolbeault, Jean
25 Duan, Renjun
24 Ha, Seung-Yeal
24 Mischler, Stéphane
23 Guillin, Arnaud
22 Kolesnikov, Alexander V.
22 Xu, Chao-Jiang
21 Carlen, Eric Anders
21 Martínez Gamba, Irene
21 Pareschi, Lorenzo
21 Wang, Feng-Yu
20 Beiglböck, Mathias
20 Bogachev, Vladimir Igorevich
20 Choi, Young-Pil
20 Strain, Robert M.
20 Yun, Seok-Bae
19 Fournier, Nicolas G.
19 Yu, Hongjun
18 Alexandre, Radjesvarane
18 Golse, François
18 Gozlan, Nathael
17 Agueh, Martial
17 Gentil, Ivan
17 Kim, Young-Heon
17 Mondino, Andrea
17 Ukai, Seiji
16 Bedrossian, Jacob
16 Cavalletti, Fabio
16 Matthes, Daniel
16 Ohta, Shin-ichi
16 Peletier, Mark Adriaan
16 Wu, Liming
15 Fathi, Max
15 Honda, Shouhei
15 Shao, Jinghai
14 Bolley, François
14 Chen, Yongxin
14 Erbar, Matthias
14 Ketterer, Christian
14 Osher, Stanley Joel
14 Velázquez, Juan J. L.
14 Vorotnikov, Dmitry A.
13 Alonso, Ricardo J.
13 Cañizo, José Alfredo
13 Fellner, Klemens
13 Ghoussoub, Nassif A.
13 Guo, Yan
13 Han-Kwan, Daniel
13 He, Lingbing
13 Hu, Jingwei
13 Li, Weixi
13 Lods, Bertrand
13 Loeper, Grégoire
13 Maas, Jan
13 Peyré, Gabriel
13 Slepčev, Dejan
13 Wolansky, Gershon
13 Zhao, Huijiang
12 Brenier, Yann
12 Briant, Marc
12 Di Francesco, Marco
12 Georgiou, Tryphon T.
12 Liu, Jianguo
12 Liu, Shuangqian
12 Loss, Michael
12 Rifford, Ludovic
12 Zanella, Mattia
12 Zhou, Hao-Min
11 Carrapatoso, Kleber
11 Cianchi, Andrea
11 Ekeland, Ivar
11 Gangbo, Wilfrid
11 Han, Bangxian
11 Jabin, Pierre-Emmanuel
11 Jourdain, Benjamin
11 Juillet, Nicolas
11 Lee, Paul W. Y.
11 Léonard, Christian
11 Lim, Yongdo
11 Lu, Xuguang
11 Masmoudi, Nader
11 Milman, Emanuel
11 Monsaingeon, Léonard
11 Nguyễn Văn Hoàng
...and 3,815 more Authors
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Cited in 453 Serials

169 Journal of Functional Analysis
147 Journal of Statistical Physics
132 Archive for Rational Mechanics and Analysis
121 Journal of Differential Equations
120 Calculus of Variations and Partial Differential Equations
101 Communications in Mathematical Physics
94 SIAM Journal on Mathematical Analysis
89 Journal of Mathematical Analysis and Applications
88 Journal de Mathématiques Pures et Appliquées. Neuvième Série
76 Kinetic and Related Models
64 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
62 Journal of Computational Physics
60 Advances in Mathematics
58 Discrete and Continuous Dynamical Systems
57 Stochastic Processes and their Applications
56 Probability Theory and Related Fields
55 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
52 The Annals of Applied Probability
49 The Annals of Probability
48 Comptes Rendus. Mathématique. Académie des Sciences, Paris
45 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
44 Journal of Mathematical Physics
43 The Journal of Geometric Analysis
39 Proceedings of the American Mathematical Society
39 Communications in Partial Differential Equations
38 Transactions of the American Mathematical Society
38 Potential Analysis
38 Bernoulli
34 SIAM Journal on Control and Optimization
34 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
33 SIAM Journal on Scientific Computing
33 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
30 Electronic Journal of Probability
28 Journal of Scientific Computing
24 Inventiones Mathematicae
24 Mathematische Annalen
22 Communications on Pure and Applied Mathematics
21 Geometric and Functional Analysis. GAFA
20 SIAM Journal on Numerical Analysis
20 Bulletin des Sciences Mathématiques
20 SIAM Journal on Imaging Sciences
20 Analysis and Geometry in Metric Spaces
19 Acta Applicandae Mathematicae
19 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
19 Electronic Journal of Statistics
18 Nonlinearity
18 The Annals of Statistics
18 Quarterly of Applied Mathematics
17 Mathematics of Computation
17 Numerische Mathematik
17 Physica D
17 Journal of Nonlinear Science
17 Journal of the European Mathematical Society (JEMS)
17 SIAM/ASA Journal on Uncertainty Quantification
17 Séminaire Laurent Schwartz. EDP et Applications
16 Applied Mathematics and Optimization
16 Memoirs of the American Mathematical Society
16 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
16 Annales Henri Poincaré
16 Communications on Pure and Applied Analysis
16 Science China. Mathematics
15 Manuscripta Mathematica
15 Statistics & Probability Letters
15 SIAM Journal on Applied Mathematics
15 Foundations of Computational Mathematics
15 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
15 Annals of PDE
14 Journal of Mathematical Imaging and Vision
14 Journal of Mathematical Sciences (New York)
14 Information Geometry
13 Bulletin of the American Mathematical Society. New Series
13 Doklady Mathematics
13 Analysis and Applications (Singapore)
12 Revista Matemática Iberoamericana
12 Communications in Contemporary Mathematics
12 Multiscale Modeling & Simulation
12 Advances in Calculus of Variations
11 Journal of Multivariate Analysis
11 Journal für die Reine und Angewandte Mathematik
11 Economic Theory
11 NoDEA. Nonlinear Differential Equations and Applications
11 Nonlinear Analysis. Real World Applications
11 Frontiers of Mathematics in China
11 SIAM Journal on Mathematics of Data Science
10 Annali di Matematica Pura ed Applicata. Serie Quarta
10 Geometriae Dedicata
10 Mathematische Zeitschrift
10 Ergodic Theory and Dynamical Systems
10 Chinese Annals of Mathematics. Series B
10 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
10 Journal of Evolution Equations
10 Discrete and Continuous Dynamical Systems. Series B
10 Entropy
10 SIAM Journal on Applied Dynamical Systems
10 Stochastics
9 Israel Journal of Mathematics
9 ZAMP. Zeitschrift für angewandte Mathematik und Physik
9 Duke Mathematical Journal
9 Journal of Optimization Theory and Applications
9 Stochastic Analysis and Applications
...and 353 more Serials
all top 5

Cited in 59 Fields

1,824 Partial differential equations (35-XX)
991 Probability theory and stochastic processes (60-XX)
820 Statistical mechanics, structure of matter (82-XX)
797 Calculus of variations and optimal control; optimization (49-XX)
548 Fluid mechanics (76-XX)
515 Differential geometry (53-XX)
421 Numerical analysis (65-XX)
315 Global analysis, analysis on manifolds (58-XX)
262 Functional analysis (46-XX)
243 Statistics (62-XX)
222 Operations research, mathematical programming (90-XX)
188 Measure and integration (28-XX)
187 Operator theory (47-XX)
184 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
173 Real functions (26-XX)
168 Dynamical systems and ergodic theory (37-XX)
166 Biology and other natural sciences (92-XX)
117 Computer science (68-XX)
114 Systems theory; control (93-XX)
97 Quantum theory (81-XX)
95 Information and communication theory, circuits (94-XX)
88 Convex and discrete geometry (52-XX)
87 Integral equations (45-XX)
71 Combinatorics (05-XX)
64 Ordinary differential equations (34-XX)
51 Mechanics of particles and systems (70-XX)
49 General topology (54-XX)
46 Potential theory (31-XX)
41 Difference and functional equations (39-XX)
39 Mechanics of deformable solids (74-XX)
38 Functions of a complex variable (30-XX)
37 Optics, electromagnetic theory (78-XX)
34 Harmonic analysis on Euclidean spaces (42-XX)
33 Relativity and gravitational theory (83-XX)
31 Geometry (51-XX)
29 Linear and multilinear algebra; matrix theory (15-XX)
28 Classical thermodynamics, heat transfer (80-XX)
22 Geophysics (86-XX)
17 Approximations and expansions (41-XX)
14 Topological groups, Lie groups (22-XX)
14 Several complex variables and analytic spaces (32-XX)
14 Astronomy and astrophysics (85-XX)
10 General and overarching topics; collections (00-XX)
10 History and biography (01-XX)
10 Number theory (11-XX)
9 Abstract harmonic analysis (43-XX)
9 Algebraic topology (55-XX)
9 Manifolds and cell complexes (57-XX)
7 Special functions (33-XX)
6 Category theory; homological algebra (18-XX)
4 Algebraic geometry (14-XX)
4 Integral transforms, operational calculus (44-XX)
3 Nonassociative rings and algebras (17-XX)
2 Mathematical logic and foundations (03-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Sequences, series, summability (40-XX)
1 Commutative algebra (13-XX)
1 Group theory and generalizations (20-XX)
1 Mathematics education (97-XX)

Citations by Year

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