Log-Sobolev inequalities for semi-direct product operators and applications

Section 3 is de- voted to obtaining the applications of the spectral inequality in control theory as observation estimates, impulse approximate controllability, null controllability

As a direct application, we derive local Strichartz estimates for randomly modulated dispersions and solve the Cauchy problem of the critical nonlinear Schrödinger equation.. Key

Inequality (38) is significant only if the Yamabe invariant is positive and in this case, the Dirac operator under the chiral bag boundary condition is invertible. So Inequality (37)

[19] Fr´ ed´ eric Robert, Existence et asymptotiques optimales des fonctions de Green des op´ erateurs elliptiques d’ordre deux (Existence and optimal asymptotics of the

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

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

For lattice spin systems with the compact spin space, remarkable progresses have been made to understand the relation between the mixing properties of the Gibbs states and the speed

The aim of this note is to investigate the relations between these cohomologies and validity of the generalized ∂ ∂-Lemma. Generalized metric and Hodge theory.. [11]), the