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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Revisiting the Glansdorff-Prigogine Criterion for Stability Within Irreversible Thermodynamics
Christian Maes,Karel Netočný +1 more
TL;DR: In this article, the authors considered the problem of approximating the Hatano-Sasa approach in irreversible thermodynamics and showed that the positivity of the excess δ 2 EP immediately implies a Clausius (in)equality for the excess heat.
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Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump
TL;DR: In this paper, the HWI inequality was generalized for the Gaussian case, and the strong Feller property, the hyper-bounded property, and some heat kernel inequalities were presented for a class of O-U type semigroups with jump.
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Talagrand’s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations*
TL;DR: In this paper, the authors established Talagrand's T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type approximations and the known results in the finite dimensional case.
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Extremal of Log Sobolev inequality and W entropy on noncompact manifolds
TL;DR: In this paper, it was shown that the Log Sobolev functional does not have an extremal function decaying exponentially near infinity under a condition near infinity, and that the extremal may not exist if the condition is violated.
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Transportation cost inequalities on path and loop groups
TL;DR: In this article, the authors defined the H-distance on the path space of a connected Lie group and established a transportation cost inequality for heat measures on the loop group Le(G).
References
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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.