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Villani, Cédric

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Author ID: villani.cedric Recent zbMATH articles by "Villani, Cédric"
Published as: Villani, C.; Villani, Cedric; Villani, Cédric
Homepage: http://cedricvillani.org
External Links: MGP · Wikidata · dblp · GND
Awards: EMS Prize (2008) · Fields Medal (2010)
Documents Indexed: 108 Publications since 1995, including 17 Books
Biographic References: 7 Publications
all top 5

Co-Authors

45 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 Cartier, Pierre
2 Dhombres, Jean G.
2 Heinzmann, Gerhard
2 Maggi, Francesco
2 Markowich, Peter Alexander
2 McCann, Robert J.
2 Ollivier, Yann
1 Ambrosio, Luigi
1 Arnold, Anton
1 Banyaga, Augustin
1 Baudoin, Edmond
1 Bodineau, Thierry
1 Brenier, Yann
1 Buttazzo, Giuseppe
1 Caffarelli, Luis Ángel
1 Caglioti, Emanuele
1 Carlen, Eric Anders
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 Gangbo, Wilfrid
1 Golse, François
1 Greuel, Gert-Martin
1 Grünberg, David
1 Grunewald, Natalie
1 Guillin, Arnaud
1 Jüngel, Ansgar
1 King, Henry C.
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 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 Székelyhidi, László jun.
1 Uzan, Jean-Philippe
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 Tohoku 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 Japanese Journal of Mathematics. 3rd Series
1 Matapli
1 La Tortue de Zénon

Publications by Year

Citations contained in zbMATH Open

86 Publications have been cited 5,876 times in 3,519 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
389
2009
A review of mathematical topics in collisional kinetic theory. Zbl 1170.82369
Villani, Cédric
325
2002
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. Zbl 0985.58019
Otto, F.; Villani, C.
264
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
158
2003
On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Zbl 0912.45011
Villani, Cédric
147
1998
Contractions in the 2-Wasserstein length space and thermalization of granular media. Zbl 1082.76105
Carrillo, José A.; McCann, Robert J.; Villani, Cédric
140
2006
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Zbl 1162.82316
Desvillettes, L.; Villani, C.
134
2005
A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Zbl 1048.26010
Cordero-Erausquin, D.; Nazaret, B.; Villani, C.
126
2004
Entropy dissipation and long-range interactions. Zbl 0968.76076
Alexandre, R.; Desvillettes, L.; Villani, C.; Wennberg, B.
108
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.
102
2001
Hypocoercivity. Zbl 1197.35004
Villani, Cédric
101
2009
On Landau damping. Zbl 1239.82017
Mouhot, Clément; Villani, Cédric
96
2011
Stability of a 4th-order curvature condition arising in optimal transport theory. Zbl 1158.53036
Villani, C.
96
2008
On the spatially homogeneous Landau equation for hard potentials. I: Existence, uniqueness and smoothness. Zbl 0946.35109
Desvillettes, Laurent; Villani, Cédric
90
2000
On the Boltzmann equation for long-range interactions. Zbl 1029.82036
Alexandre, R.; Villani, C.
66
2002
On the spatially homogeneous Landau equation for hard potentials. II: H-theorem and applications. Zbl 0951.35130
Desvillettes, Laurent; Villani, Cédric
63
2000
Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. Zbl 0958.82044
Toscani, G.; Villani, C.
63
1999
Weak curvature conditions and functional inequalities. Zbl 1119.53028
Lott, John; Villani, Cédric
61
2007
Quantitative concentration inequalities for empirical measures on non-compact spaces. Zbl 1113.60093
Bolley, François; Guillin, Arnaud; Villani, Cédric
60
2007
Cercignani’s conjecture is sometimes true and always almost true. Zbl 1041.82018
Villani, Cédric
60
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.; Salsa, S. (ed.); Villani, Cédric
53
2003
Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Zbl 1063.76086
Mouhot, Clément; Villani, Cédric
51
2004
On the Boltzmann equation for diffusively excited granular media. Zbl 1106.82031
Gamba, I. M.; Panferov, V.; Villani, C.
50
2004
On the Landau approximation in plasma physics. Zbl 1044.83007
Alexandre, R.; Villani, C.
50
2004
On the spatially homogeneous Landau equation for Maxwellian molecules. Zbl 0957.82029
Villani, C.
50
1998
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Zbl 1087.60008
Bolley, François; Villani, Cédric
45
2005
Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Zbl 0944.35066
Toscani, G.; Villani, C.
39
1999
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. Zbl 1273.76373
Gamba, I. M.; Panferov, V.; Villani, C.
36
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
36
2009
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.
35
2000
Entropy and chaos in the Kac model. Zbl 1186.76675
Carlen, Eric A.; Carvalho, Maria C.; Le Roux, Jonathan; Loss, Michael; Villani, Cédric
33
2010
On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. Zbl 1034.82032
Toscani, G.; Villani, C.
33
2000
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.
30
2004
Regularity of optimal transport in curved geometry: the nonfocal case. Zbl 1192.53041
Loeper, Grégoire; Villani, Cédric
29
2010
Mathematics of granular materials. Zbl 1134.82040
Villani, Cédric
29
2006
On the Cauchy problem for Landau equations: Sequential stability, global existence. Zbl 0856.35020
Villani, Cédric
29
1996
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
On a variant of Korn’s inequality arising in statistical mechanics. Zbl 1092.82032
Desvillettes, L.; Villani, Cédric
27
2002
Hamilton-Jacobi semigroup on length spaces and applications. Zbl 1210.53047
Lott, John; Villani, Cédric
26
2007
Nearly round spheres look convex. Zbl 1241.53031
Figalli, Alessio; Rifford, Ludovic; Villani, Cedric
25
2012
Hypocoercive diffusion operators. Zbl 1130.35027
Villani, Cédric
24
2006
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
23
2011
Balls have the worst best Sobolev inequalities. Zbl 1086.46021
Maggi, Francesco; Villani, Cédric
22
2005
A short proof of the “concavity of entropy power”. Zbl 0994.94018
Villani, Cédric
22
2000
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Zbl 0934.45010
Villani, Cédric
22
1999
On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
20
2010
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Zbl 1106.65324
Pareschi, L.; Toscani, G.; Villani, C.
18
2003
Fisher information estimates for Boltzmann’s collision operator. Zbl 0918.60093
Villani, C.
17
1998
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.
15
2012
Landau damping. Zbl 1247.82081
Mouhot, Clément; Villani, Cédric
15
2010
Celebrating Cercignani’s conjecture for the Boltzmann equation. Zbl 1217.82064
Desvillettes, Laurent; Mouhot, Clément; Villani, Cédric
14
2011
Balls have the worst best Sobolev inequalities. II: Variants and extensions. Zbl 1135.46016
Maggi, F.; Villani, C.
13
2008
Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Zbl 1301.58017
Bodineau, Thierry; Lebowitz, Joel; Mouhot, Clément; Villani, Cédric
11
2014
Entropy production and convergence to equilibrium. Zbl 1128.76056
Villani, Cédric
10
2008
Optimal regularity for square roots. Zbl 0870.35017
Lions, Pierre-Louis; Villani, Cédric
10
1995
Trend to equilibrium for dissipative equations, functional inequalities and mass transportation. Zbl 1134.35375
Villani, Cédric
9
2004
An approximation lemma about the cut locus, with applications in optimal transport theory. Zbl 1172.53022
Figalli, Alessio; Villani, Cédric
7
2008
Comment on “Hypercontractivity of Hamilton-Jacobi equations” by S. G. Bobkov, I. Gentil and M. Ledoux. Zbl 1134.35312
Otto, Felix; Villani, Cédric
7
2001
Conservative forms of Boltzmann’s collision operator: Landau revisited. Zbl 0919.35140
Villani, Cédric
7
1999
Regularity of optimal transport and cut locus: from nonsmooth analysis to geometry to smooth analysis. Zbl 1225.49048
Villani, Cédric
6
2011
\(H\)-theorem and beyond: Boltzmann’s entropy in today’s mathematics. Zbl 1156.82313
Villani, Cédric
6
2008
Hydrodynamic limits of Boltzmann’s equation (following C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). Zbl 1119.82037
Villani, Cédric
6
2002
Decrease of the Fisher information for solutions of the spatially homogeneous Landau equation with Maxwellian molecules. Zbl 1010.82023
Villani, C.
6
2000
Synthetic theory of Ricci curvature bounds. Zbl 1353.53019
Villani, Cédric
5
2016
Optimal transportation, dissipative PDE’s and functional inequalities. Zbl 1039.35147
Villani, Cedric
5
2003
Homogeneous cooling states are not always good approximations to granular flows. Zbl 1053.74012
Caglioti, E.; Villani, C.
5
2002
Entropic methods for the study of the long time behavior of kinetic equations. Zbl 1038.82073
Desvillettes, L.; Villani, C.
5
2001
Tangent cut loci on surfaces. Zbl 1217.53038
Figalli, A.; Rifford, L.; Villani, C.
4
2011
Hypocoercive diffusion operators. Zbl 1178.35306
Villani, Cédric
4
2007
Optimal transport. Theory and applications. Proceedings of the summer school ‘Optimal transportation: theory and applications’, Fourier Institute, Grenoble, France. Zbl 1301.00076
Ollivier, Yann (ed.); Pajot, Hervé (ed.); Villani, Cédric (ed.)
3
2014
The living theorem. Zbl 1290.01002
Villani, Cédric
3
2012
Optimal transport and Ricci curvature. Zbl 1141.53030
Villani, Cédric
3
2006
Entropy production and convergence to equilibrium for the Boltzmann equation. Zbl 1221.82082
Villani, Cédric
3
2005
(Ir)reversibility and entropy. Zbl 1320.82036
Villani, Cédric
2
2013
Landau damping. Zbl 1307.76087
Villani, Cédric
2
2013
Optimal transport and curvature. Zbl 1247.53003
Figalli, Alessio; Villani, Cédric
2
2011
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; Golse, François (ed.); Olla, Stefano (ed.)
2
2008
Strong displacement convexity on Riemannian manifolds. Zbl 1125.53026
Figalli, A.; Villani, C.
2
2007
(Ir)reversibility and entropy. Zbl 1259.82089
Villani, Cédric
1
2012
Landau damping. Zbl 1230.82042
Villani, Cédric
1
2011
The Scheffer-Shnirelman paradox revisited from the viewpoint of convex integration (after C. De Lellis and L. Szḱelyhidi). Zbl 1404.35338
Villani, Cédric
1
2010
Rate of convergence toward the equilibrium in degenerate settings. Zbl 1069.35011
Desvillettes, L.; Villani, C.
1
2004
On the inelastic Boltzmann equation with diffusive forcing. Zbl 1032.76065
Gamba, Irene M.; Panferov, Vladislav; Villani, Cedric
1
2002
On the trend to equilibrium for kinetic equations. Zbl 1128.82303
Villani, C.
1
2002
Synthetic theory of Ricci curvature bounds. Zbl 1353.53019
Villani, Cédric
5
2016
Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Zbl 1301.58017
Bodineau, Thierry; Lebowitz, Joel; Mouhot, Clément; Villani, Cédric
11
2014
Optimal transport. Theory and applications. Proceedings of the summer school ‘Optimal transportation: theory and applications’, Fourier Institute, Grenoble, France. Zbl 1301.00076
Ollivier, Yann (ed.); Pajot, Hervé (ed.); Villani, Cédric (ed.)
3
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
25
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.
15
2012
The living theorem. Zbl 1290.01002
Villani, Cédric
3
2012
(Ir)reversibility and entropy. Zbl 1259.82089
Villani, Cédric
1
2012
On Landau damping. Zbl 1239.82017
Mouhot, Clément; Villani, Cédric
96
2011
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
23
2011
Celebrating Cercignani’s conjecture for the Boltzmann equation. Zbl 1217.82064
Desvillettes, Laurent; Mouhot, Clément; Villani, Cédric
14
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
2
2011
Landau damping. Zbl 1230.82042
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
33
2010
Regularity of optimal transport in curved geometry: the nonfocal case. Zbl 1192.53041
Loeper, Grégoire; Villani, Cédric
29
2010
On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034
Figalli, Alessio; Rifford, Ludovic; Villani, Cédric
20
2010
Landau damping. Zbl 1247.82081
Mouhot, Clément; Villani, Cédric
15
2010
The Scheffer-Shnirelman paradox revisited from the viewpoint of convex integration (after C. De Lellis and L. Szḱelyhidi). 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
389
2009
Hypocoercivity. Zbl 1197.35004
Villani, Cédric
101
2009
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. Zbl 1273.76373
Gamba, I. M.; Panferov, V.; Villani, C.
36
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
36
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.
96
2008
Balls have the worst best Sobolev inequalities. II: Variants and extensions. Zbl 1135.46016
Maggi, F.; Villani, C.
13
2008
Entropy production and convergence to equilibrium. Zbl 1128.76056
Villani, Cédric
10
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
6
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; Golse, François (ed.); Olla, Stefano (ed.)
2
2008
Weak curvature conditions and functional inequalities. Zbl 1119.53028
Lott, John; Villani, Cédric
61
2007
Quantitative concentration inequalities for empirical measures on non-compact spaces. Zbl 1113.60093
Bolley, François; Guillin, Arnaud; Villani, Cédric
60
2007
Hamilton-Jacobi semigroup on length spaces and applications. Zbl 1210.53047
Lott, John; Villani, Cédric
26
2007
Hypocoercive diffusion operators. Zbl 1178.35306
Villani, Cédric
4
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
140
2006
Mathematics of granular materials. Zbl 1134.82040
Villani, Cédric
29
2006
Hypocoercive diffusion operators. Zbl 1130.35027
Villani, Cédric
24
2006
Optimal transport and Ricci curvature. 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.
134
2005
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities. Zbl 1087.60008
Bolley, François; Villani, Cédric
45
2005
Balls have the worst best Sobolev inequalities. Zbl 1086.46021
Maggi, Francesco; Villani, Cédric
22
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.
126
2004
Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. Zbl 1063.76086
Mouhot, Clément; Villani, Cédric
51
2004
On the Boltzmann equation for diffusively excited granular media. Zbl 1106.82031
Gamba, I. M.; Panferov, V.; Villani, C.
50
2004
On the Landau approximation in plasma physics. Zbl 1044.83007
Alexandre, R.; Villani, C.
50
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.
30
2004
Trend to equilibrium for dissipative equations, functional inequalities and mass transportation. Zbl 1134.35375
Villani, Cédric
9
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
158
2003
Cercignani’s conjecture is sometimes true and always almost true. Zbl 1041.82018
Villani, Cédric
60
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.; Salsa, S. (ed.); Villani, Cédric
53
2003
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit. Zbl 1106.65324
Pareschi, L.; Toscani, G.; Villani, C.
18
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
325
2002
On the Boltzmann equation for long-range interactions. Zbl 1029.82036
Alexandre, R.; Villani, C.
66
2002
On a variant of Korn’s inequality arising in statistical mechanics. Zbl 1092.82032
Desvillettes, L.; Villani, Cédric
27
2002
Hydrodynamic limits of Boltzmann’s equation (following C. Bardos, F. Golse, C. D. Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). Zbl 1119.82037
Villani, Cédric
6
2002
Homogeneous cooling states are not always good approximations to granular flows. Zbl 1053.74012
Caglioti, E.; Villani, C.
5
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 equilibrium for kinetic equations. Zbl 1128.82303
Villani, C.
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.
102
2001
Comment on “Hypercontractivity of Hamilton-Jacobi equations” by S. G. Bobkov, I. Gentil and M. Ledoux. Zbl 1134.35312
Otto, Felix; Villani, Cédric
7
2001
Entropic methods for the study of the long time behavior of kinetic equations. Zbl 1038.82073
Desvillettes, L.; Villani, C.
5
2001
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. Zbl 0985.58019
Otto, F.; Villani, C.
264
2000
Entropy dissipation and long-range interactions. Zbl 0968.76076
Alexandre, R.; Desvillettes, L.; Villani, C.; Wennberg, B.
108
2000
On the spatially homogeneous Landau equation for hard potentials. I: Existence, uniqueness and smoothness. Zbl 0946.35109
Desvillettes, Laurent; Villani, Cédric
90
2000
On the spatially homogeneous Landau equation for hard potentials. II: H-theorem and applications. Zbl 0951.35130
Desvillettes, Laurent; Villani, Cédric
63
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.
35
2000
On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. Zbl 1034.82032
Toscani, G.; Villani, C.
33
2000
A short proof of the “concavity of entropy power”. Zbl 0994.94018
Villani, Cédric
22
2000
Decrease of the Fisher information for solutions of the spatially homogeneous Landau equation with Maxwellian molecules. Zbl 1010.82023
Villani, C.
6
2000
Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. Zbl 0958.82044
Toscani, G.; Villani, C.
63
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.
39
1999
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Zbl 0934.45010
Villani, Cédric
22
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
147
1998
On the spatially homogeneous Landau equation for Maxwellian molecules. Zbl 0957.82029
Villani, C.
50
1998
Fisher information estimates for Boltzmann’s collision operator. Zbl 0918.60093
Villani, C.
17
1998
On the Cauchy problem for Landau equations: Sequential stability, global existence. Zbl 0856.35020
Villani, Cédric
29
1996
Optimal regularity for square roots. Zbl 0870.35017
Lions, Pierre-Louis; Villani, Cédric
10
1995
all top 5

Cited by 3,398 Authors

90 Carrillo de la Plata, José Antonio
39 Figalli, Alessio
39 Toscani, Giuseppe
37 Mouhot, Clément
35 Ambrosio, Luigi
35 Villani, Cédric
35 Yang, Tong
33 Sturm, Karl-Theodor
29 Gigli, Nicola
29 Santambrogio, Filippo
28 Morimoto, Yoshinori
27 Desvillettes, Laurent
27 Savaré, Giuseppe
26 McCann, Robert J.
25 Carlier, Guillaume
25 Wang, Feng-Yu
23 Duan, Renjun
23 Xu, Chao-Jiang
22 Dolbeault, Jean
22 Guillin, Arnaud
22 Mischler, Stéphane
21 Martínez Gamba, Irene
21 Kolesnikov, Alexander V.
21 Li, Wuchen
20 Carlen, Eric Anders
19 Pareschi, Lorenzo
19 Strain, Robert M.
18 Agueh, Martial
18 Alexandre, Radjesvarane
18 Ha, Seung-Yeal
18 Yu, Hongjun
18 Yun, Seok-Bae
17 Bogachev, Vladimir Igorevich
17 Gentil, Ivan
17 Kim, Young-Heon
17 Ukai, Seiji
16 Gozlan, Nathael
16 Mondino, Andrea
16 Peletier, Mark Adriaan
16 Wu, Liming
15 Beiglböck, Mathias
15 Fournier, Nicolas G.
15 Shao, Jinghai
14 Cañizo, José Alfredo
14 Erbar, Matthias
14 Fathi, Max
14 Guo, Yan
14 Matthes, Daniel
14 Ohta, Shin-ichi
13 Alonso, Ricardo J.
13 Bedrossian, Jacob
13 Bolley, François
13 Di Francesco, Marco
13 Ghoussoub, Nassif A.
13 Lods, Bertrand
13 Maas, Jan
13 Peyré, Gabriel
13 Slepčev, Dejan
13 Velázquez, Juan J. L.
13 Wolansky, Gershon
13 Zhao, Huijiang
12 Cavalletti, Fabio
12 Chen, Yongxin
12 Choi, Young-Pil
12 Fellner, Klemens
12 Golse, François
12 Honda, Shouhei
12 Liu, Jianguo
12 Liu, Shuangqian
12 Pavliotis, Grigorios A.
12 Rifford, Ludovic
12 Vorotnikov, Dmitry A.
11 Brenier, Yann
11 Briant, Marc
11 Ekeland, Ivar
11 Gangbo, Wilfrid
11 Georgiou, Tryphon T.
11 Ketterer, Christian
11 Ledoux, Michel
11 Lee, Paul W. Y.
11 Léonard, Christian
11 Li, Weixi
11 Lim, Yongdo
11 Rossi, Julio Daniel
11 Schlichting, André
10 Blanchet, Adrien
10 Cianchi, Andrea
10 Galichon, Alfred
10 Gallouët, Thomas O.
10 He, Lingbing
10 Hu, Jingwei
10 Jabin, Pierre-Emmanuel
10 Loeper, Grégoire
10 Loss, Michael
10 Lu, Xuguang
10 Malrieu, Florent
10 Mazón Ruiz, José M.
10 Otto, Felix
10 Piccoli, Benedetto
10 Rajala, Tapio
...and 3,298 more Authors
all top 5

Cited in 407 Serials

154 Journal of Functional Analysis
128 Journal of Statistical Physics
117 Archive for Rational Mechanics and Analysis
115 Journal of Differential Equations
108 Calculus of Variations and Partial Differential Equations
89 Communications in Mathematical Physics
82 SIAM Journal on Mathematical Analysis
80 Journal de Mathématiques Pures et Appliquées. Neuvième Série
79 Journal of Mathematical Analysis and Applications
65 Kinetic and Related Models
57 Advances in Mathematics
57 Stochastic Processes and their Applications
56 Discrete and Continuous Dynamical Systems
51 Journal of Computational Physics
51 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
49 Probability Theory and Related Fields
48 Comptes Rendus. Mathématique. Académie des Sciences, Paris
45 The Annals of Probability
45 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
43 Journal of Mathematical Physics
43 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
39 The Annals of Applied Probability
38 Communications in Partial Differential Equations
35 Potential Analysis
34 Proceedings of the American Mathematical Society
33 The Journal of Geometric Analysis
32 Transactions of the American Mathematical Society
29 Bernoulli
28 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
27 SIAM Journal on Control and Optimization
26 SIAM Journal on Scientific Computing
25 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
23 Mathematische Annalen
22 Communications on Pure and Applied Mathematics
21 Inventiones Mathematicae
21 Geometric and Functional Analysis. GAFA
20 Journal of Scientific Computing
20 Bulletin des Sciences Mathématiques
18 Electronic Journal of Probability
18 SIAM Journal on Imaging Sciences
17 SIAM Journal on Numerical Analysis
17 Analysis and Geometry in Metric Spaces
16 Acta Applicandae Mathematicae
16 Journal of the European Mathematical Society (JEMS)
15 Mathematics of Computation
15 Quarterly of Applied Mathematics
15 Statistics & Probability Letters
15 Physica D
15 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
14 Journal of Multivariate Analysis
14 Manuscripta Mathematica
14 Memoirs of the American Mathematical Society
14 SIAM Journal on Applied Mathematics
14 Communications on Pure and Applied Analysis
14 Electronic Journal of Statistics
14 Science China. Mathematics
13 Nonlinearity
13 Numerische Mathematik
13 Journal of Mathematical Sciences (New York)
13 Annales Henri Poincaré
12 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
12 Bulletin of the American Mathematical Society. New Series
12 Journal of Mathematical Imaging and Vision
12 Journal of Nonlinear Science
12 Doklady Mathematics
12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
11 The Annals of Statistics
11 Economic Theory
11 Multiscale Modeling & Simulation
11 Analysis and Applications (Singapore)
11 SIAM/ASA Journal on Uncertainty Quantification
11 Séminaire Laurent Schwartz. EDP et Applications
10 Applied Mathematics and Optimization
10 Geometriae Dedicata
10 Journal für die Reine und Angewandte Mathematik
10 Ergodic Theory and Dynamical Systems
10 Applied Mathematics Letters
10 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
10 Communications in Contemporary Mathematics
10 Entropy
10 SIAM Journal on Applied Dynamical Systems
9 ZAMP. Zeitschrift für angewandte Mathematik und Physik
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 Duke Mathematical Journal
9 Journal of Optimization Theory and Applications
9 Chinese Annals of Mathematics. Series B
9 Stochastic Analysis and Applications
9 Applied and Computational Harmonic Analysis
9 NoDEA. Nonlinear Differential Equations and Applications
9 Electronic Communications in Probability
9 Foundations of Computational Mathematics
9 Discrete and Continuous Dynamical Systems. Series B
9 Advances in Calculus of Variations
8 Mathematische Zeitschrift
8 Discrete & Computational Geometry
8 Revista Matemática Iberoamericana
8 European Journal of Applied Mathematics
8 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
8 Journal of Evolution Equations
8 Frontiers of Mathematics in China
...and 307 more Serials
all top 5

Cited in 59 Fields

1,561 Partial differential equations (35-XX)
832 Probability theory and stochastic processes (60-XX)
715 Statistical mechanics, structure of matter (82-XX)
655 Calculus of variations and optimal control; optimization (49-XX)
491 Fluid mechanics (76-XX)
434 Differential geometry (53-XX)
344 Numerical analysis (65-XX)
271 Global analysis, analysis on manifolds (58-XX)
222 Functional analysis (46-XX)
179 Operations research, mathematical programming (90-XX)
178 Statistics (62-XX)
156 Operator theory (47-XX)
152 Measure and integration (28-XX)
152 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
150 Real functions (26-XX)
147 Dynamical systems and ergodic theory (37-XX)
140 Biology and other natural sciences (92-XX)
101 Systems theory; control (93-XX)
82 Information and communication theory, circuits (94-XX)
80 Convex and discrete geometry (52-XX)
80 Quantum theory (81-XX)
76 Integral equations (45-XX)
71 Computer science (68-XX)
55 Ordinary differential equations (34-XX)
53 Combinatorics (05-XX)
49 Mechanics of particles and systems (70-XX)
42 General topology (54-XX)
36 Potential theory (31-XX)
36 Mechanics of deformable solids (74-XX)
31 Difference and functional equations (39-XX)
29 Optics, electromagnetic theory (78-XX)
28 Geometry (51-XX)
27 Functions of a complex variable (30-XX)
27 Harmonic analysis on Euclidean spaces (42-XX)
25 Relativity and gravitational theory (83-XX)
23 Linear and multilinear algebra; matrix theory (15-XX)
22 Classical thermodynamics, heat transfer (80-XX)
17 Geophysics (86-XX)
14 Topological groups, Lie groups (22-XX)
12 Astronomy and astrophysics (85-XX)
11 Several complex variables and analytic spaces (32-XX)
10 History and biography (01-XX)
8 Abstract harmonic analysis (43-XX)
8 Manifolds and cell complexes (57-XX)
7 Number theory (11-XX)
7 Approximations and expansions (41-XX)
7 Algebraic topology (55-XX)
6 General and overarching topics; collections (00-XX)
6 Special functions (33-XX)
5 Category theory; homological algebra (18-XX)
3 Mathematical logic and foundations (03-XX)
3 Nonassociative rings and algebras (17-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Algebraic geometry (14-XX)
2 Integral transforms, operational calculus (44-XX)
1 Commutative algebra (13-XX)
1 Group theory and generalizations (20-XX)
1 Sequences, series, summability (40-XX)
1 Mathematics education (97-XX)

Citations by Year

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