Logarithmic Sobolev inequalities for mollified compactly supported measures

Compactly supported wavelet bases for Sobolev spaces

In this paper we investigate compactly supported wavelet bases for Sobolev spaces. Starting with a pair of compactly supported refinable functions φ and φ̃ in L2(R) satisfying a very mild condition, we provide a general principle for constructing a wavelet ψ such that the wavelets ψjk := 2j/2ψ(2j · − k) (j, k ∈ Z) form a Riesz basis for L2(R). If, in addition, φ lies in the Sobolev space H(R), t...

Modified logarithmic Sobolev inequalities and transportation inequalities

Isoperimetry and Symmetrization for Logarithmic Sobolev Inequalities

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.

Logarithmic Sobolev Inequalities for Inhomogeneous Markov Semigroups

We investigate the dissipativity properties of a class of scalar second order parabolic partial differential equations with time-dependent coefficients. We provide explicit condition on the drift term which ensure that the relative entropy of one particular orbit with respect to some other one decreases to zero. The decay rate is obtained explicitly by the use of a Sobolev logarithmic inequalit...

Logarithmic Sobolev inequalities for some nonlinear PDE’s

The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac Kean-Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with quadratic cost; on the other hand, the propagation of chaos for particle systems in mean field in...