Nonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequality

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar´e inequality (for instance logarithmic Sobolev or F -Sobolev).. The case

In Section 3, we present the proof of Theorem 1.2, and as an application, we explain how to use the parabolic Kozono-Taniuchi inequality in order to prove the long time existence

In the general case, inequality proved in this article, we do not know if the modified logarithmic Sobolev inequality (2.9) implies transportation inequality (2.16).... Using Theorem

Key words : Nonlinear wave equations, Cauchy problem, Strichartz’ estimate, minimal regularity, homogeneous Besov

We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of

Second, a spectral gap or a logarithmic Sobolev inequality, uniform over the density, for a Glauber dynamics on one site which is reversible with respect to the one-site marginal of

Classically, finite modified logarithmic Sobolev inequalities are used to deduce a differential inequality for the evolution of the relative entropy with respect to the

In fact when a probability measure is more log-concave than the Gaussian measure, we obtain a modified logarithmic Sobolev inequality sharper than the classical inequality of