Yet Another Proof of the Entropy Power Inequality

Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or R\'enyi entropies. The proof is based on a simple change of variables, is formally identical in one and several dimensions, and easily settles the equality case

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.Comment: Only change: replaced Isometry by Isoperimetry in html page. the file is the sam

Pointwise Symmetrization Inequalities for Sobolev functions and applications

We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equationsComment: made a number of corrections, added some reference

Elliptic boundary value problems with measurable coefficients and explosive boundary conditions

This Phd thesis follows two different directions, always related to elliptic boundary value problems. The first one concerns existence and regularity results for a wide class of non coercive operators with convection or drift lower order terms. The second one focuses on asymptotic behaviour of large solutions, namely solutions that blows up to infinity at the boundary of the domain, to semilinear elliptic problems