Comparison Results for a Class of Variational Inequalities

Sin resume

Existence results for a class of degenerate elliptic equations

In the present paper we prove existence results for a class of nonlinear elliptic equations whose prototype is -div (|D u|^(p−2) Du ϕ( x) ) + |D u|^σ ϕ( x)= g ϕ ; where Ω is an open set, u=0 on \partial Ω; the function ϕ( x) = (2π)^ (n/2) exp (−|x|2 /2) is the density of Gauss measure and g \in the weighted Lorentz-Zygmund space L^r (log L)^(-1/2) (ϕ,Ω), 1<r<p’. The results are sharp in this class of spaces

Linear elliptic equations related to Gauss measure

In this paper we study a Dirichlet problem relative to the equation Lu = g \phi - (f_i \phi)(x_i), where L is a linear elliptic operator with lower-order terms whose ellipticity condition is given in terms of the function \phi(x), the density of the Gaussian measure

Weighted isoperimetric inequalities on R^n and applications to rearrangements

We study isoperimetric inequalities for a certain class of probability measures on R^n together with applications to integral inequalities for weighted rearrangements. Furthermore, we compare the solution to a linear elliptic problem with the solution to some “rearranged” problem defined in the domain x : x_1 < α(x_2 , . . . , x_n) with a suitable function α(x_2 , . . . , x_n )

Some Remarks on the Stability of the Log-Sobolev Inequality for the Gaussian Measure

This note consists of two parts. Firstly, we bound the deficit in the logarithmic Sobolev Inequality and in the Talagrand transport-entropy Inequality for the Gaussian measure, in any dimension, by means of a distance introduced by Bucur and Fragalà. Thereafter, we investigate the stability issue with tools from Fourier analysis