Related papers: Logarithmic Sobolev inequality revisited
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.
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…
This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants.
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…
In this paper we present our results on the logarithmic Sobolev inequality along the Ricci flow in dimension 2.
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Pr\'ekopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly convex…
In this article we present Sobolev-type inequalities for the localization of pseudo-relativistic energy.
We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.
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 G\"{o}tze. Under mild assumptions the condition is also necessary.…
We obtain some new inequalities of Chebyshev Type.
We provide a proof of the sharp log-Sobolev inequality on a compact interval.
We present a class of modified logarithmic Sobolev inequality, interpolating between Poincar\'e and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or more complex $\exp(-|x|^\al\log^\beta(2+|x|))$…
We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in GAFA (2000). We prove by Prekopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on $\dR^n$.…
The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances.
In this note, we characterize the equality case of the sharp $L^2$-Euclidean logarithmic Sobolev inequality with monomial weights, exploiting the idea by Bobkov and Ledoux \cite{Bob}. Our approach is new even in the unweighted case. Also,…
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
We give complete details on an alternative formulation of the Polya-Szego principle that was mentioned in Remark 1 of our paper "Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities". We also provide an alternative proof to…
We discuss new proofs, and new forms, of a reverse logarithmic Sobolev inequality, with respect to the standard Gaussian measure, for low complexity functions, measured in terms of Gaussian-width. In particular, we provide a dimension-free…
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