Gradient flows in metric spaces and in the space of probability measures, La méthode de Beckner est basée sur une décomposition du noyau en série de fonctions sphériques harmoniques, ce qui permet de calculer ensuite Lectures in Mathematics ETH Zürich, 2008. ,
Sharp Sobolev Inequalities on the Sphere and the Moser--Trudinger Inequality, The Annals of Mathematics, vol.138, issue.1 ,
DOI : 10.2307/2946638
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000. ,
DOI : 10.1007/s002110050002
Semianalytic and subanalytic sets, Publications math??matiques de l'IH??S, vol.41, issue.2, pp.5-42, 1988. ,
DOI : 10.1007/BF02699126
Existence and nonexistence of solutions for a model of gravitational interaction of particles, III. Colloq. Math, vol.68, issue.2, pp.229-239, 1995. ,
The 8??-problem for radially symmetric solutions of a chemotaxis model in the plane, Mathematical Methods in the Applied Sciences, vol.8, issue.13, pp.1563-1583, 2006. ,
DOI : 10.1002/mma.743
Existence and nonexistence of solutions for a model of gravitational interaction of particles, I. Colloq. Math, vol.66, issue.2, pp.319-334, 1994. ,
Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak???Keller???Segel Model, SIAM Journal on Numerical Analysis, vol.46, issue.2, pp.691-721, 2008. ,
DOI : 10.1137/070683337
Functional inequalities, thick tails and asymptotics for the critical mass Patlak???Keller???Segel model, Journal of Functional Analysis, vol.262, issue.5, pp.2142-2230, 2012. ,
DOI : 10.1016/j.jfa.2011.12.012
URL : https://hal.archives-ouvertes.fr/hal-00512743
Critical mass for a Patlak???Keller???Segel model with degenerate diffusion in higher dimensions, Calculus of Variations and Partial Differential Equations, vol.61, issue.1, pp.133-168, 2009. ,
DOI : 10.1007/s00526-008-0200-7
URL : https://hal.archives-ouvertes.fr/hal-00626990
Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions, Electron. J. Differential Equations, vol.32, issue.44, p.pp, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00113519
Convexity of injectivity domains on the ellipsoid of revolution: The oblate case, Comptes Rendus Mathematique, vol.348, issue.23-24, pp.23-241315, 2010. ,
DOI : 10.1016/j.crma.2010.10.036
URL : https://hal.archives-ouvertes.fr/hal-00545768
Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris Sér. I Math, vol.305, pp.805-808, 1987. ,
Diffusion, attraction and collapse, Nonlinearity, vol.12, issue.4, pp.1071-1098, 1999. ,
DOI : 10.1088/0951-7715/12/4/320
Analyse fonctionnelle Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications. [Theory and applications], 1983. ,
Simplicial structure of the real analytic cut locus, Proc. Amer, pp.118-121, 1977. ,
DOI : 10.1090/S0002-9939-1977-0474133-5
Boundary regularity of maps with convex potentials, Communications on Pure and Applied Mathematics, vol.5, issue.9, pp.1141-1151, 1992. ,
DOI : 10.1002/cpa.3160450905
The regularity of mappings with a convex potential, Journal of the American Mathematical Society, vol.5, issue.1, pp.99-104, 1992. ,
DOI : 10.1090/S0894-0347-1992-1124980-8
Boundary regularity of maps with convex potentials, Communications on Pure and Applied Mathematics, vol.5, issue.9, pp.453-496, 1996. ,
DOI : 10.1002/cpa.3160450905
The Monge Ampere equation and optimal transportation, Contemp. Math. Amer. Math. Soc, vol.353, pp.43-52, 2004. ,
DOI : 10.1090/conm/353/06430
Fully nonlinear elliptic equations, 1995. ,
DOI : 10.1090/coll/043
Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities, Proc. Amer, pp.3515-3530, 2012. ,
DOI : 10.1090/S0002-9939-2012-11306-1
URL : https://hal.archives-ouvertes.fr/hal-00503203
Blow-up, Concentration Phenomenon and Global Existence for the Keller???Segel Model in High Dimension, Communications in Partial Differential Equations, vol.8, issue.4, pp.561-584, 2012. ,
DOI : 10.1016/j.jde.2010.02.008
URL : https://hal.archives-ouvertes.fr/hal-00462450
Modified Keller-Segel system and critical mass for the log interaction kernel In Stochastic analysis and partial differential equations Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on S n, Contemp. Math. Amer. Math. Soc. Geom. Funct. Anal, vol.429, issue.21, pp.45-6290, 1992. ,
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller???Segel equation, Duke Mathematical Journal, vol.162, issue.3, 2012. ,
DOI : 10.1215/00127094-2019931
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Revista Matem??tica Iberoamericana, vol.19, issue.3, pp.971-1018, 2003. ,
DOI : 10.4171/RMI/376
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media, Archive for Rational Mechanics and Analysis, vol.179, issue.2, pp.217-263, 2006. ,
DOI : 10.1007/s00205-005-0386-1
Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.3, pp.695-718, 2010. ,
DOI : 10.1051/cocv/2009020
URL : https://hal.archives-ouvertes.fr/hal-00923303
Nonlinear aspects of chemotaxis, Mathematical Biosciences, vol.56, issue.3-4, pp.217-237, 1981. ,
DOI : 10.1016/0025-5564(81)90055-9
Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions, Milan Journal of Mathematics, vol.72, issue.1, pp.1-28, 2004. ,
DOI : 10.1007/s00032-003-0026-x
Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Amp??re operator, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.8, issue.5, pp.443-457, 1991. ,
DOI : 10.1016/S0294-1449(16)30256-6
Locally nearly spherical surfaces are almost-positively $c$-curved, Methods and Applications of Analysis, vol.18, issue.3, 2010. ,
DOI : 10.4310/MAA.2011.v18.n3.a2
Regularity of optimal transport on compact, locally nearly spherical, manifolds, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2010, issue.646, pp.65-115, 2010. ,
DOI : 10.1515/crelle.2010.066
Gradient estimates for potentials of invertible gradient???mappings on the sphere, Calculus of Variations and Partial Differential Equations, vol.487, issue.3, pp.297-311, 2006. ,
DOI : 10.1007/s00526-006-0006-4
Modélisation, analyse mathématique et simulation numérique de problèmes issus de la biologie, 2010. ,
Symmetrization Techniques on Unbounded Domains: Application to a Chemotaxis System on RN, Journal of Differential Equations, vol.145, issue.1, pp.156-183, 1998. ,
DOI : 10.1006/jdeq.1997.3389
Optimal critical mass in the two dimensional Keller???Segel model in, Comptes Rendus Mathematique, vol.339, issue.9, pp.611-616, 2004. ,
DOI : 10.1016/j.crma.2004.08.011
The two-dimensional Keller-Segel model after blow-up, Discrete and Continuous Dynamical Systems, vol.25, issue.1 ,
DOI : 10.3934/dcds.2009.25.109
URL : https://hal.archives-ouvertes.fr/hal-00158767
Continuity and injectivity of optimal maps for non-negatively cross-curved costs, 2009. ,
Regularity of optimal transport maps on multiple products of spheres, Journal of the European Mathematical Society, vol.15, issue.4, 2010. ,
DOI : 10.4171/JEMS/388
Hölder continuity and injectivity of optimal maps, 2011. ,
DOI : 10.1007/s00205-013-0629-5
URL : http://arxiv.org/abs/1107.1014
When is multidimensional screening a convex program?, Journal of Economic Theory, vol.146, issue.2, pp.454-478, 2011. ,
DOI : 10.1016/j.jet.2010.11.006
URL : http://arxiv.org/abs/0912.3033
C 1 regularity of solutions of the Monge???Amp??re equation for optimal transport in dimension two, Calculus of Variations and Partial Differential Equations, vol.123, issue.3, pp.537-550, 2009. ,
DOI : 10.1007/s00526-009-0222-9
Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds, Tohoku Mathematical Journal, vol.63, issue.4, pp.855-876, 2011. ,
DOI : 10.2748/tmj/1325886291
URL : https://hal.archives-ouvertes.fr/hal-00923320
Nearly Round Spheres Look Convex, American Journal of Mathematics, vol.134, issue.1, pp.109-139, 2012. ,
DOI : 10.1353/ajm.2012.0000
URL : https://hal.archives-ouvertes.fr/hal-00923321
An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory, Methods and Applications of Analysis, vol.15, issue.2, pp.149-154, 2008. ,
DOI : 10.4310/MAA.2008.v15.n2.a3
A finite volume scheme for the Patlak???Keller???Segel chemotaxis model, Numerische Mathematik, vol.146, issue.N 37(4, pp.457-488, 2006. ,
DOI : 10.1007/s00211-006-0024-3
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis, Mathematische Nachrichten, vol.17, issue.1, pp.77-114, 1998. ,
DOI : 10.1002/mana.19981950106
Riemannian geometry. Universitext, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00002870
Asymptotically self-similar blow-up of semilinear heat equations, Communications on Pure and Applied Mathematics, vol.38, issue.3 ,
DOI : 10.1002/cpa.3160380304
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System, Journal of Statistical Physics, vol.206, issue.4, pp.133-151, 2009. ,
DOI : 10.1007/s10955-009-9717-1
Convergence of a Stochastic Particle Approximation for Measure Solutions of the 2D Keller-Segel System, Communications in Partial Differential Equations, vol.9, issue.6, pp.940-960, 2011. ,
DOI : 10.1016/j.jde.2004.05.013
Finite-time aggregation into a single point in a reaction - diffusion system, Nonlinearity, vol.10, issue.6, pp.1739-1754, 1997. ,
DOI : 10.1088/0951-7715/10/6/016
Chemotactic collapse for the Keller-Segel model, Journal of Mathematical Biology, vol.35, issue.2, pp.177-194, 1996. ,
DOI : 10.1007/s002850050049
Singularity patterns in a chemotaxis model, Mathematische Annalen, vol.XXI, issue.Fasc. 4, pp.583-623, 1996. ,
DOI : 10.1007/BF01445268
Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding, Advances in Applied Mathematics, vol.26, issue.4, pp.280-301, 2001. ,
DOI : 10.1006/aama.2001.0721
A user???s guide to PDE models for chemotaxis, Journal of Mathematical Biology, vol.15, issue.1, pp.183-217, 2009. ,
DOI : 10.1007/s00285-008-0201-3
From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. I. Jahresber, Deutsch. Math.-Verein, vol.105, issue.3, pp.103-165, 2003. ,
Boundedness vs. blow-up in a chemotaxis system, Journal of Differential Equations, vol.215, issue.1, pp.52-107, 2005. ,
DOI : 10.1016/j.jde.2004.10.022
The Lipschitz continuity of the distance function to the cut locus, Transactions of the American Mathematical Society, vol.353, issue.01, pp.21-40, 2001. ,
DOI : 10.1090/S0002-9947-00-02564-2
On explosions of solutions to a system of partial differential equations modelling chemotaxis, Transactions of the American Mathematical Society, vol.329, issue.2, pp.819-824, 1992. ,
DOI : 10.1090/S0002-9947-1992-1046835-6
The Variational Formulation of the Fokker--Planck Equation, SIAM Journal on Mathematical Analysis, vol.29, issue.1, pp.1-17, 1998. ,
DOI : 10.1137/S0036141096303359
On a Problem of Monge, Journal of Mathematical Sciences, vol.133, issue.4 ,
DOI : 10.1007/s10958-006-0050-9
On mass transportation, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat ,
Initiation of slime mold aggregation viewed as an instability, Journal of Theoretical Biology, vol.26, issue.3, pp.399-415, 1970. ,
DOI : 10.1016/0022-5193(70)90092-5
Model for chemotaxis, Journal of Theoretical Biology, vol.30, issue.2, pp.225-234, 1971. ,
DOI : 10.1016/0022-5193(71)90050-6
Traveling bands of chemotactic bacteria: A theoretical analysis, Journal of Theoretical Biology, vol.30, issue.2 ,
DOI : 10.1016/0022-5193(71)90051-8
Counterexamples to Continuity of Optimal Transport Maps on Positively Curved Riemannian Manifolds, International Mathematics Research Notices, vol.15, 2008. ,
DOI : 10.1093/imrn/rnn120
On the cost-subdifferentials of cost-convex functions, 2007. ,
Continuity, curvature, and the general covariance of optimal transportation, Journal of the European Mathematical Society, vol.12, issue.4, pp.1009-1040, 2010. ,
DOI : 10.4171/JEMS/221
Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular), Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2012, issue.664, pp.1-27, 2012. ,
DOI : 10.1515/CRELLE.2011.105
The Ma???Trudinger???Wang curvature for natural mechanical actions, Calculus of Variations and Partial Differential Equations, vol.8, issue.1, pp.285-299, 2011. ,
DOI : 10.1007/s00526-010-0362-y
The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations, Communications on Pure and Applied Mathematics, vol.15, issue.1, pp.85-146, 2005. ,
DOI : 10.1002/cpa.20051
Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities ,
Hölder regularity of optimal mappings in optimal transportation. Calc Var, Partial Differential Equations, vol.34, pp.435-451, 2009. ,
Regularity for Potential Functions in Optimal Transportation, Communications in Partial Differential Equations, vol.46, issue.1, pp.165-184, 2010. ,
DOI : 10.1007/s11401-006-0142-3
On the regularity of solutions of optimal transportation problems, Acta Mathematica, vol.202, issue.2, pp.241-283, 2009. ,
DOI : 10.1007/s11511-009-0037-8
Regularity of optimal transport in curved geometry: The nonfocal case, Duke Mathematical Journal, vol.151, issue.3, pp.431-485, 2010. ,
DOI : 10.1215/00127094-2010-003
Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.3, pp.597-621, 2006. ,
DOI : 10.1051/m2an:2006025
Regularity of Potential Functions of the Optimal Transportation Problem, Archive for Rational Mechanics and Analysis, vol.13, issue.2, pp.151-183, 2005. ,
DOI : 10.1007/s00205-005-0362-9
Critical Point Theory for Lagrangian Systems, Progress in Mathematics. Birkhäuser, vol.293, 2012. ,
DOI : 10.1007/978-3-0348-0163-8
A convexity principle for interacting gases Polar factorization of maps on Riemannian manifolds, Adv. Math. Geom. Funct. Anal, vol.12888, issue.113, pp.153-179589, 1997. ,
Stability of the blow-up profile for equations of the type u t = ?u + |u| p?1 u. Duke Math, J, vol.86, issue.1, pp.143-195, 1997. ,
Mémoire sur la théorie des deblais et des remblais Histoire de l'académie royale des sciences de Paris, pp.666-704, 1781. ,
Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math ,
Blowup in infinite time in the simplified system of chemotaxis, Adv. Math. Sci. Appl, vol.17, issue.2, pp.445-472, 2007. ,
THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION, Communications in Partial Differential Equations, vol.4, issue.1-2 ,
DOI : 10.1007/BF00535689
Volume-filling and quorum-sensing in models for chemosensitive movement, Can. Appl. Math. Q, vol.10, issue.4, pp.501-543, 2002. ,
Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, vol.198, issue.3, pp.311-338, 1953. ,
DOI : 10.1007/BF02476407
PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic, Applications of Mathematics, vol.49, issue.6 ,
DOI : 10.1007/s10492-004-6431-9
Transport equations in biology, Frontiers in mathematics. Birkhäuser, 2006. ,
Riemannian geometry ,
A Jacobian Inequality for Gradient Maps on the Sphere and Its Application to Directional Statistics, Communications in Statistics - Theory and Methods, vol.42, issue.14, 2009. ,
DOI : 10.1007/978-3-540-71050-9
Blowup of radial solutions to a parabolic-elliptic system related to chemotaxis, Bull. Kyushu Inst. Technol. Pure Appl. Math, issue.58, pp.1-11, 2011. ,
Chemotactic collapse of radial solutions to Jäger-Luckhaus system ,
On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.65-131, 2006. ,
DOI : 10.1007/s11511-006-0002-8
On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.133-177, 2006. ,
DOI : 10.1007/s11511-006-0002-8
Free energy and self-interacting particles Progress in Nonlinear Differential Equations and their Applications, 2005. ,
On the second boundary value problem for Monge- Ampère type equations and optimal transportation, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.8, issue.51, pp.143-174, 2009. ,
On the second boundary value problem for equations of Monge-Ampère type, J ,
THE SECOND BOUNDARY VALUE PROBLEM FOR A CLASS OF HESSIAN EQUATIONS, Communications in Partial Differential Equations, vol.46, issue.5-6, pp.859-882, 2001. ,
DOI : 10.1007/s005260050097
Stability of Some Mechanisms of Chemotactic Aggregation, SIAM Journal on Applied Mathematics, vol.62, issue.5 ,
DOI : 10.1137/S0036139900380049
Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions, SIAM Journal on Applied Mathematics, vol.64, issue.4, pp.1224-1248, 2004. ,
DOI : 10.1137/S003613990343389X
Optimal transport, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2009. ,
DOI : 10.1007/978-3-540-71050-9
URL : https://hal.archives-ouvertes.fr/hal-00974787