共查询到20条相似文献,搜索用时 15 毫秒
1.
CHEN Mufa 《中国科学A辑(英文版)》2000,43(6):601-608
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. 相似文献
2.
Jian WANG 《Frontiers of Mathematics in China》2009,4(4):721-726
We give two examples to show that the strong ergodicity and the logarithmic Sobolev inequality are incomparable for ergodic
birth-death processes. 相似文献
3.
Ralph Howard 《Proceedings of the American Mathematical Society》1998,126(9):2779-2787
Let be a complete two dimensional simply connected Riemannian manifold with Gaussian curvature . If is a compactly supported function of bounded variation on , then satisfies the Sobolev inequality
Conversely, letting be the characteristic function of a domain recovers the sharp form of the isoperimetric inequality for simply connected surfaces with . Therefore this is the Sobolev inequality ``equivalent' to the isoperimetric inequality for this class of surfaces. This is a special case of a result that gives the equivalence of more general isoperimetric inequalities and Sobolev inequalities on surfaces.
Under the same assumptions on , if is a closed curve and is the winding number of about , then the Sobolev inequality implies
which is an extension of the Banchoff-Pohl inequality to simply connected surfaces with curvature .
4.
Motivated by the rate at which the entropy of an ergodic Markov chain relative to its stationary distribution decays to zero,
we study modified versions of logarithmic Sobolev inequalities in the discrete setting of finite Markov chains and graphs.
These inequalities turn out to be weaker than the standard log-Sobolev inequality, but stronger than the Poincare’ (spectral
gap) inequality. We show that, in contrast with the spectral gap, for bounded degree expander graphs, various log-Sobolev
constants go to zero with the size of the graph. We also derive a hypercontractivity formulation equivalent to our main modified
log-Sobolev inequality. Along the way we survey various recent results that have been obtained in this topic by other researchers.
相似文献
5.
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo. 相似文献
6.
Angela Alberico Teresa Alberico Carlo Sbordone 《Nonlinear Analysis: Theory, Methods & Applications》2012
We give a Sobolev inequality with the weight K(x) belonging to the class A2∩Gn for the function |u|t and the weight K(x)−1 for |∇u|2. The constant in the relevant inequality is seen to depend on the Gn and A2 constants of the weight. 相似文献
7.
PhilippeBIANE 《数学学报(英文版)》2003,19(3):497-506
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 Poincare-type inequality. 相似文献
8.
Andrea Cianchi 《Journal of Functional Analysis》2006,237(2):466-481
A quantitative version of the standard Sobolev inequality, with sharp constant, for functions u in W1,1(Rn) (or BV(Rn)) is established in terms of a distance of u from the manifold of all multiples of characteristic functions of balls. Inequalities involving non-Euclidean norms of the gradient are discussed as well. 相似文献
9.
We provide a new characterization of the logarithmic Sobolev inequality. 相似文献
10.
本文在有限von Neumann代数生成的非交换概率空间L~p(p≥1)框架下,证明了一类量子Markov半群的超压缩性等价于其对应的Dirichlet型满足对数Sobolev不等式.此结果包含前人的相关成果为特例.作为推论,细化了Biane的相关工作. 相似文献
11.
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various
sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev case. The idea
behind many of these conditions is that measures with a non-convex potential may enjoy such functional inequalities provided
they have a strong integrability property that balances the lack of convexity. In addition, several known criteria are recovered
in a simple unified way by transportation methods and generalized to the Riemannian setting.
The research of A.V. Kolesnikov was supported by RFBR 07-01-00536, DFG Grant 436 RUS 113/343/0 and GFEN 06-01-39003. 相似文献
12.
Julian Fernndez Bonder Enrique Lami Dozo Julio D. Rossi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2004,21(6):261-805
In this article we study symmetry properties of the extremals for the Sobolev trace embedding H1(B(0,μ))Lq(∂B(0,μ)) with 1q2(N−1)/(N−2) for different values of μ. These extremals u are solutions of the problem We find that, for 1q<2(N−1)/(N−2), there exists a unique normalized extremal u, which is positive and has to be radial, for μ small enough. For the critical case, q=2(N−1)/(N−2), as a consequence of the symmetry properties for small balls, we conclude the existence of radial extremals. Finally, for 1<q2, we show that a radial extremal exists for every ball. 相似文献
13.
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000) 191-200] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems. 相似文献
14.
生灭过程与一维扩散过程的对数sobolev不等式 总被引:1,自引:0,他引:1
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。 相似文献
15.
Zhonghai Ding 《Proceedings of the American Mathematical Society》1996,124(2):591-600
A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on . It is proved that the trace operator is a linear bounded operator from to for .
16.
Julián Fernández Bonder Nicolas Saintier 《Annali di Matematica Pura ed Applicata》2008,187(4):683-704
In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality that are independent of Ω. This estimates generalized those of Adimurthi and Yadava (Comm Partial Diff Equ 16(11):1733–1760,
1991) for general p. Here p
* : = p(N − 1)/(N − p) is the critical exponent for the immersion and N is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic
problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of Fernández Bonder
and Rossi (Bull Lond Math Soc 37:119–125, 2005). Finally, we study an optimal design problem with critical exponent.
相似文献
17.
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others
functional inequalities (weak Poincaré inequalities, general Beckner inequalities, etc.). We also discuss the quantitative
behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré
inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
相似文献
18.
Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts. 相似文献
19.
Sufficient conditions for the existence of extremal functions in the trace Sobolev inequality and the trace Sobolev-Poincaré inequality are established. It is shown that some of these conditions are sharp. 相似文献
20.
In this article, motivated by a work of Caffarelli and Cordoba in phase transitions analysis, we prove new weighted anisotropic Sobolev type inequalities where different derivatives have different weight functions. These inequalities are also intimately connected to weighted Sobolev inequalities for Grushin type operators, the weights being not necessarily Muckenhoupt. For example we consider Sobolev inequalities on finite cylinders, the weight being a power of the distance function from the top or the bottom of the cylinder. We also prove similar inequalities in the more general case in which the weight is a power of the distance function from a higher codimension part of the boundary. 相似文献