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Villani, Cédric

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 Author ID: villani.cedric 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
all top 5

Fields

 49 Statistical mechanics, structure of matter (82-XX) 41 Partial differential equations (35-XX) 33 Fluid mechanics (76-XX) 18 History and biography (01-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 18 Differential geometry (53-XX) 14 Probability theory and stochastic processes (60-XX) 10 General and overarching topics; collections (00-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Functional analysis (46-XX) 6 Operations research, mathematical programming (90-XX) 5 Measure and integration (28-XX) 5 Integral equations (45-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 4 Information and communication theory, circuits (94-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 2 Mechanics of deformable solids (74-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)

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

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