共查询到20条相似文献,搜索用时 109 毫秒
1.
Young Ja Park 《Proceedings of the American Mathematical Society》2004,132(7):2075-2083
A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.
2.
Sharp asymptotic information is determined for the Gagliardo–Nirenberg embedding constants in high dimension. This analysis is motivated by the earlier observation that the logarithmic Sobolev inequality controls the Nash inequality. Moreover, one sees here that Hardy's inequality can be interpreted as the asymptotic limit of the logarithmic Sobolev inequality. 相似文献
3.
Liming Wu 《Probability Theory and Related Fields》2000,118(3):427-438
By means of the martingale representation, we establish a new modified logarithmic Sobolev inequality, which covers the previous
modified logarithmic Sobolev inequalities of Bobkov-Ledoux and the L
1-logarithmic Sobolev inequality obtained in our previous work. From it we derive several sharp deviation inequalities of Talagrand's
type, by following the powerful Herbst method developed recently by Ledoux and al. Moreover this new modified logarithmic
Sobolev inequality is transported on the discontinuous path space with respect to the law of a Lévy process.
Received: 16 June 1999 / Revised version: 13 March 2000 / Published online: 12 October 2000 相似文献
4.
Doklady Mathematics - A sharp integral inequality is proved that is used to derive a Sobolev interpolation inequality. A generalization of the logarithmic Sobolev inequality is proposed based on... 相似文献
5.
In this paper, we obtain the uniform logarithmic Sobolev inequality for the Boltzmann measures by reducing multi-dimensional
measures to one-dimensional measures, and then applying the characterization on the constant of logarithmic Sobolev inequality
for a probability measure on the real line. 相似文献
6.
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
7.
Michel Ledoux 《Comptes Rendus Mathematique》2005,340(4):301-304
We present a one-dimensional version of the functional form of the geometric Brunn–Minkowski inequality in free (non-commutative) probability theory. The proof relies on matrix approximation as used recently by Biane and Hiai et al. to establish free analogues of the logarithmic Sobolev and transportation cost inequalities for strictly convex potentials, that are recovered here from the Brunn–Minkowski inequality as in the classical case. The method is used to extend to the free setting the Otto–Villani theorem stating that the logarithmic Sobolev inequality implies the transportation cost inequality. To cite this article: M. Ledoux, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
8.
Sobolev type inequalities for general symmetric forms 总被引:5,自引:0,他引:5
Feng-Yu Wang 《Proceedings of the American Mathematical Society》2000,128(12):3675-3682
A general version of the Sobolev type inequality, including both the classical Sobolev inequality and the logarithmic Sobolev one, is studied for general symmetric forms by using isoperimetric constants. Some necessary and sufficient conditions are presented as results. The main results are illustrated by two examples of birth-death processes.
9.
Yong-Hua Mao 《Journal of Mathematical Analysis and Applications》2008,338(2):1092-1099
A general Sobolev type inequality is introduced and studied for general symmetric forms by defining a new type of Cheeger's isoperimetric constant. Finally, concentration of measure for the Lp type logarithmic Sobolev inequality is presented. 相似文献
10.
Jie Xiao 《Bulletin des Sciences Mathématiques》2006,130(1):87
We establish a sharp Sobolev trace inequality for the fractional-order derivatives. As a close connection with this best estimate, we show a fractional-order logarithmic Sobolev trace inequality with the asymptotically optimal constant, but also sharpen the Poincaré embedding for the conformal invariant energy and BMO spaces. 相似文献
11.
Fred B Weissler 《Journal of Functional Analysis》1980,37(2):218-234
A logarithmic Sobolev inequality, analogous to Gross' inequality, is proved on the circle. From this inequality it follows that the Poisson and heat semigroups on the circle satisfy Nelson's hypercontractive estimates. 相似文献
12.
《高校应用数学学报(英文版)》2021,36(2)
Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemannian 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. 相似文献
13.
Chengjie Yu 《manuscripta mathematica》2010,132(3-4):295-306
In this article, we get a time-dependent Sobolev inequality along the Ricci flow in a more general situation than those in Zhang (A uniform Sobolev inequality under Ricci flow. Int Math Res Not IMRN 2007, no 17, Art ID rnm056, 17 pp), Ye (The logarithmic Sobolev inequality along the Ricci flow. arXiv:0707.2424v2) and Hsu (Uniform Sobolev inequalities for manifolds evolving by Ricci flow. arXiv:0708.0893v1) which also generalizes the results of them. As an application of the time-dependent Sobolev inequality, we get a growth of the ratio of non-collapsing along immortal solutions of Ricci flow. 相似文献
14.
S. Artstein-Avidan B. Klartag C. Schütt E. Werner 《Journal of Functional Analysis》2012,262(9):4181-4204
We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure. 相似文献
15.
Ivan Gentil 《Bulletin des Sciences Mathématiques》2002,126(6):507-524
Following the equivalence between logarithmic Sobolev inequality, hypercontractivity of the heat semigroup showed by Gross and hypercontractivity of Hamilton-Jacobi equations, we prove, like the Varopoulos theorem, the equivalence between Euclidean-type Sobolev inequality and an ultracontractive control of the Hamilton-Jacobi equations. We obtain also ultracontractive estimations under general Sobolev inequality which imply in the particular case of a probability measure, transportation inequalities. 相似文献
16.
The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature 下载免费PDF全文
The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional
curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a
recent result of Brendle with Euclidean setting. 相似文献
17.
Manuel del Pino Stathis Filippas Achilles Tertikas 《Journal of Functional Analysis》2010,259(8):2045-2072
We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy. This inequality differs from standard logarithmic Sobolev inequalities in the sense that the measure is neither Lebesgue's measure nor a probability measure. All terms are scale invariant. After an Emden-Fowler transformation, the inequality can be rewritten as an optimal inequality of logarithmic Sobolev type on the cylinder. Explicit expressions of the sharp constant, as well as minimizers, are established in the radial case. However, when no symmetry is imposed, the sharp constants are not achieved by radial functions, in some range of the parameters. 相似文献
18.
Mathematical Notes - A sharp integral inequality is proved and used to obtain a Sobolev interpolation inequality. Further, a new proof of a Gross-Sobolev logarithmic inequality is constructed on... 相似文献
19.
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
20.
Elena Pelliccia Giorgio Talenti 《Calculus of Variations and Partial Differential Equations》1993,1(3):237-242
A proof is offered which links a logarithmic Sobolev inequality with an isoperimetric inequality by Borell and Ehrhardt. 相似文献