共查询到20条相似文献,搜索用时 15 毫秒
1.
The classical Sobolev embedding theorem of the space of functions of bounded variation BV(Rn) into Ln′(Rn) is proved in a sharp quantitative form. 相似文献
2.
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
3.
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
4.
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.
5.
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
6.
7.
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
8.
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations. 相似文献
9.
K. Watanabe Y. Kametaka K. Takemura 《Journal of Mathematical Analysis and Applications》2008,340(1):699-706
The best constants Cm,j of Sobolev embedding of Hm(0,a) into Cj[0,a](0?j?m−1) are obtained. Especially, when a=∞, these constants can be represented in a closed form. 相似文献
10.
We revisit two results of [3]; they are a logarithmic Sobolev inequality on Rn with Lipschitz constants and an expression of Lipschitz constants as the limit of a functional by the entropy. We have two goals in this paper. The first goal is to clarify when the strict inequality holds in this inequality. The second goal is to investigate the asymptotic behavior of this functional by the Abelian and Tauberian theorems of Laplace transforms. 相似文献
11.
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
12.
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
13.
14.
Shuxuan Li 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3716-3727
In this paper, taking the Hessian Sobolev inequality (0<p≤k) (X.-J. Wang, 1994 [2]) as the starting point, we give a proof of the Hessian Sobolev inequality when k<p≤k∗, where k∗ is the critical Sobolev embedding index of k-Hessian type. We also prove that k∗ is optimal by one-dimensional Hardy’s inequality. 相似文献
15.
The deficit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances. 相似文献
16.
This paper generalizes an inequality of Moser from the case that is in the Lebesgue space to certain subspaces, namely the Lorentz spaces , where . The conclusion is that is integrable, where . This is a higher degree of integrability than in the Moser inequality when . A formula for is given and it is also shown that no larger value of works.
17.
Felix Otto 《Journal of Functional Analysis》2007,243(1):121-157
We give a criterion for the logarithmic Sobolev inequality (LSI) on the product space X1×?×XN. We have in mind an N-site lattice, unbounded continuous spin variables, and Glauber dynamics. The interactions are described by the Hamiltonian H of the Gibbs measure. The criterion for LSI is formulated in terms of the LSI constants of the single-site conditional measures and the size of the off-diagonal entries of the Hessian of H. It is optimal for Gaussians with positive covariance matrix. To illustrate, we give two applications: one with weak interactions and one with strong interactions and a decay of correlations condition. 相似文献
18.
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
19.
Sanja Maruši? 《Journal of Mathematical Analysis and Applications》2002,272(2):575-581
In this paper we study the asymptotic behaviour of the constants in Sobolev inequalities in thin domains with respect to the thickness of the domain ε. We prove that the sharp Sobolev constants in thin domains converge to the sharp Sobolev constant on the lower-dimensional domain, as ε tends to zero. 相似文献
20.
Ivan Gentil 《Journal of Functional Analysis》2003,202(2):591-599
We prove a general optimal Lp-Euclidean logarithmic Sobolev inequality by using Prékopa-Leindler inequality and a special Hamilton-Jacobi equation. In particular we generalize the inequality proved by Del Pino and Dolbeault in (J. Funt. Anal.). 相似文献