Asymptotic behaviour of reversible chemical reaction-diffusion equations

We investigate the asymptotic behavior of the a large class of reversible chemical reaction-diffusion equations with the same diffusion. In particular we prove the optimal rate in two cases : when there is no diffusion and in the classical "two-by-two" case

Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups

We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such inequalities to hold and discuss relations between various classes of inequalities

Coercive Inequalities on Metric Measure Spaces

We study coercive inequalities on finite dimensional metric spaces with probability measures which do not have volume doubling property. This class of inequalities includes Poincar\'e and Log-Sobolev inequality. Our main result is proof of Log-Sobolev inequality on Heisenberg group equipped with either heat kernel measure or "gaussian" density build from optimal control distance. As intermediate results we prove so called U-bounds

From U-bounds to isoperimetry with applications to H-type groups

In this paper we study applications of U-bounds to coercive and isoperimetric problems for probability measures on finite and infinite products of H-type groups.Comment: 40 pages, with addition

Markov semigroups with hypocoercive-type generator in Infinite Dimensions: Ergodicity and Smoothing

We start by considering infinite dimensional Markovian dynamics in R^m generated by operators of hypocoercive type and for such models we obtain short and long time pointwise estimates for all the derivatives, of any order and in any direction, along the semigroup. We then look at infinite dimensional models (in (Rm)^{Z ^d}) produced by the interaction of infinitely many finite dimensional dissipative dynamics of the type indicated above. For these infinite dimensional models we study finite speed of propagation of information, well-posedness of the semigroup, time behaviour of the derivatives and strong ergodicity problem