THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

Rearrangement and the weighted logarithmic Sobolev inequality

Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemanian manifolds.We give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sobolev inequality is true and obtain a new estimate on the entropy.

Logarithmic Sobolev Inequalities for Two-Sided Birth-Death Processes

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for a is also presented.

Logarithmic Sobolev inequality for symmetric forms

Some estimates of logarithmic Sobolev constant for general symmetric forms are obtained in terms of new Cheeger’s constants. The estimates can be sharp in some sense.

The Logarithmic Sobolev Inequality Along the Ricci Flow:The Caseλ0(g0)=0

A uniform logarithmic Sobolev inequality,a uniform Sobolev inequality and a uniformκ-noncollapsing estimate along the Ricci flow are established in the situation that a certain smallest eigenvalue for the initial metric is zero.

A Stein deficit for the logarithmic Sobolev inequality

We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.

The Equivalence of Hypercontractivity and Logarithmic Sobolev Inequality for q(-1≤q≤1)-Ornstein-Uhlenbeck Semigroup

In this paper the author proves the equivalence of hypercontractivity and logarithmic Sobolev inequality for q-Ornstein-Uhlenbeck semigroup Ut(q)=Γq(e-tI)(-1≤q≤1),whereΓq is a q-Gaussian functor.

生灭过程与一维扩散过程的对数Sobolev不等式(英文)

本文运用加权的Ｈａｒｄｙ不等式的方法给出了生灭过程与一维扩散过程满足对数Ｓｏｂｏｌｅｖ不等式的显式判别准则．

Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.

Cantor集上的对数Sobolev不等式

利用两点不等式和构造一类特殊的映射的方法，证明了一类特殊集合—Cantor集上的标准Laplace算子满足对数Sobolev不等式，并给出相应的对数Sobolev常数的估计．

扩散过程轨道空间上的对数Sobolev不等式(英语)

设M是连通Riemann流形,Z是M上C′类向量场,L=(△+Z),本文使用Kendall的耦合分析,给出了参考测度为L-扩散过程在t时刻分布的对数Sobolev常数的估计,并由此建立了轨道空间上的对数Sobolev不等式。此外,本文还给出了流形上的对数Sobolev常数的一个上界估计,所获结果,是对文[1],[2]和[3]的相应结果的推广。

对数各向异性Sobolev不等式

利用Hlder不等式,分别结合各向异性Sobolev不等式和带权各向异性Sobolev不等式,得到了对数各向异性Sobolev不等式和对数带权各向异性Sobolev不等式,从而将对数Sobolev不等式推广到对数各向异性情形.

环上含参变量的Boltzmann测度的对数Sobolev不等式

本文主要研究环上的含参变量h的Boltzmann测度μh的对数Sobolev不等式.通过降维方法以及对该不等式最佳常数CLS(μh)的估计,证明了该测度关于h满足一致的对数Sobolev不等式,且对数Sobolev最佳常数CLS(μh)在h>0时是具有常数阶的.结合已有的结果,再次佐证对数Sobolev不等式严格强于Talagrand传输不等式以及Poincare不等式.

Logarithmic Sobolev Inequalities, Matrix Models and Free Entropy

We give two applications of logarithmic Sobolev inequalities to matrix models and free probability. We also provide a new characterization of semi-circular systems through a Poincaré-type inequality.

Poincaréand Logarithmic Sobolev Inequalities for Nearly Radial Measures

Poincaréinequality has been studied by Bobkov for radial measures,but few are known about the logarithmic Sobolev inequality in the radial case.We try to fill this gap here using different methods:Bobkov's argument and super-Poincaréinequalities,direct approach via L_(1)-logarithmic Sobolev inequalities.We also give various examples where the obtained bounds are quite sharp.Recent bounds obtained by Lee–Vempala in the log-concave bounded case are refined for radial measures.

The Logarithmic Sobolev and Sobolev Inequalities Along the Ricci Flow

Based on Perelman’s entropy monotonicity,uniform logarithmic Sobolev inequalities along the Ricci flow are derived.Then uniform Sobolev inequalities along theRicci floware derived via harmonic analysis of the integral transform of the relevant heat operator.These inequalities are fundamental analytic properties of the Ricci flow.They are also extended to the volume-normalized Ricci flow and the Kähler-Ricci flow.

圈上Moebius测度的Sobolev不等式（英文）

本文考虑单位圈上的Moebius测度的问题.利用文献[1]和[2]中的方法,把圈上的Moebius测度的估计转化为对一维扩散过程的相关估计上,得到了单位圈上的Moebius测度的Poincar不等式,对数Sobolev不等式和Sobolev不等式的最佳常数的双边估计.

Talagrand's T_2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

我们与锋利的常数为无限的维的消散的散开建立 Talagrand 的 T_2 交通不平等，通过 Galerkin 类型在有限维的盒子中的近似和已知的结果。而且，在添加剂噪音盒子中，我们与锋利的常数证明也对数的 Sobolev 是不平等。到 Reaction-Diffusionequations 的应用被提供。

独立随机变量函数的集中不等式

目的对独立随机变量函数的指数距进行研究。方法利用由Ledoux和Massart给出的对数Sobolev不等式。结果给出了一个新的集中不等式,此不等式可看作是E fron-Sein不等式的指数形式。结论给出的新的集中不等式容易应用,可应用于其他方向的研究。

非牛顿多方渗流方程解的有界性估计

首先利用对数索伯列夫不等式,经过较为复杂的运算,构造了一个特殊的一阶常微分方程,然后利用一阶常微分方程解对初值的依赖性,对具有Lr初值的非牛顿多方渗流方程的齐边值问题给出了解的有界性估计.