A family of functional inequalities: Łojasiewicz inequalities and displacement convex functions

[1]  Jüngel , 2020 .

[2]  Bruce W. Suter,et al.  From error bounds to the complexity of first-order descent methods for convex functions , 2015, Math. Program..

[3]  F. Santambrogio.  Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , 2015 .

[4]  Filippo Santambrogio,et al.  Optimal Transport for Applied Mathematicians , 2015 .

[5]  Optimal transport and Rényi informational divergence , 2015 .

[6]  Dirk Helbing,et al.  Modelling and Optimisation of Flows on Networks , 2013 .

[7]  L. Ambrosio,et al.  A User’s Guide to Optimal Transport , 2013 .

[8]  From log Sobolev to Talagrand: A quick proof , 2012 .

[9]  Asuka Takatsu,et al.  Displacement convexity of generalized relative entropies , 2010, 1005.1331.

[10]  Christian L'eonard,et al.  Transport Inequalities. A Survey , 2010, 1003.3852.

[11]  J. Bolte,et al.  Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity , 2009 .

[12]  Adrian S. Lewis,et al.  Clarke Subgradients of Stratifiable Functions , 2006, SIAM J. Optim..

[13]  J. Vázquez.  The Porous Medium Equation: Mathematical Theory , 2006 .

[14]  C. Villani,et al.  Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media , 2006 .

[15]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[16]  A. Guillin,et al.  Transportation cost-information inequalities and applications to random dynamical systems and diffusions , 2004, math/0410172.

[17]  C. Villani,et al.  Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates , 2003 .

[18]  C. Villani.  Topics in Optimal Transportation , 2003 .

[19]  Christian Houdré,et al.  Inequalities for generalized entropy and optimal transportation , 2003 .

[20]  Manuel del Pino,et al.  Best constants for Gagliardo–Nirenberg inequalities and applications to nonlinear diffusions☆ , 2002 .

[21]  Ralph Chill,et al.  On the Łojasiewicz–Simon gradient inequality , 2003 .

[22]  S. Bobkov,et al.  Hypercontractivity of Hamilton-Jacobi equations , 2001 .

[23]  Ansgar Jüngel,et al.  Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities , 2001 .

[24]  F. Otto.  THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .

[25]  M. Ledoux.  The concentration of measure phenomenon , 2001 .

[26]  C. Villani,et al.  Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality , 2000 .

[27]  J. A. Carrillo,et al.  Asymptotic L1-decay of solutions of the porous medium equation to self-similarity , 2000 .

[28]  Alain Haraux,et al.  Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity , 1999 .

[29]  K. Kurdyka.  On gradients of functions definable in o-minimal structures , 1998 .

[30]  R. McCann.  A Convexity Principle for Interacting Gases , 1997 .

[31]  W. Gangbo,et al.  The geometry of optimal transportation , 1996 .

[32]  D. Kinderlehrer,et al.  THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .

[33]  M. Ledoux.  Inégalités isopérimétriques en analyse et probabilités , 1993 .

[34]  L. Caffarelli.  Boundary regularity of maps with convex potentials , 1992 .

[35]  Y. Brenier.  Polar Factorization and Monotone Rearrangement of Vector-Valued Functions , 1991 .

[36]  D. Stroock,et al.  Logarithmic Sobolev inequalities and stochastic Ising models , 1987 .

[37]  L. Simon.  Asymptotics for a class of non-linear evolution equations, with applications to geometric problems , 1983 .

[38]  P. Meyer,et al.  Sur les inegalites de Sobolev logarithmiques. I , 1982 .

[39]  S. Łojasiewicz.  Ensembles semi-analytiques , 1965 .