Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Felix Otto,Cédric Villani +1 more
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In this paper, it was shown that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587-600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities.About:
This article is published in Journal of Functional Analysis.The article was published on 2000-06-01 and is currently open access. It has received 1080 citations till now. The article focuses on the topics: Sobolev inequality & Interpolation inequality.read more
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Distance, energy, and dissipation in gradient flow systems
TL;DR: In this paper, an outline and reference list from a course taught in the Winter School at the University of Wurzburg in February, 2014 is presented, along with a course description.
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Finer estimates on the 2-dimensional matching problem
Luigi Ambrosio,Federico Glaudo +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of the expected cost of the random matching problem on a 2-dimensional compact manifold, improving in several aspects the results of L. Ambrosio, F. Stra and D. Trevisan.
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Convexity of mutual information along the Ornstein-Uhlenbeck flow
Andre Wibisono,Varun Jog +1 more
TL;DR: In this article, the authors studied the convexity of mutual information as a function of time along the flow of the Ornstein-Uhlenbeck process and proved that mutual information is eventually convex, i.e., convex for all large time.
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The large time profile for Hamilton–Jacobi–Bellman equations
TL;DR: In this paper, the authors study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton-Jacobi-Bellman equations with convex Hamiltonians in the torus.
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One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities
TL;DR: In this paper , the problem of trend to equilibrium for one-dimensional Fokker-Planck equations modeling socio-economic problems, and functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails are discussed.
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Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
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Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
TL;DR: In this paper, it was shown that for every vector-valued function u Lp(X, p; Rd) there is a unique polar factorization u = V$.s, where $ is a convex function defined on R and s is a measure-preserving mapping from (x, p) into (Q, I. I), provided that u is nondegenerate.
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The geometry of dissipative evolution equations: the porous medium equation
TL;DR: In this paper, the authors show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural, and they use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
Book
Topological methods in hydrodynamics
Vladimir I. Arnold,Boris Khesin +1 more
TL;DR: A group theoretical approach to hydrodynamics is proposed in this article, where the authors consider the hydrodynamic geometry of diffeomorphism groups and the principle of least action implies that the motion of a fluid is described by geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy.
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The variational formulation of the Fokker-Planck equation
TL;DR: The Fokker-Planck equation as mentioned in this paper describes the evolution of the probability density for a stochastic process associated with an Ito Stochastic Differential Equation.