In this paper, we present recent stability results with explicit and dimensionally sharp
constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic …

Stability for the logarithmic Sobolev inequality - ScienceDirect Skip to main contentSkip to
article Elsevier logo Journals & Books Help Search My account Sign in View PDF Download full …

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A
quantitative version proven by Carlen with a remainder involving the Fourier–Wiener …

We study quantitative stability results for different classes of Sobolev inequalities on general
compact Riemannian manifolds. We prove that, up to constants depending on the manifold …

In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions
to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log …

This thesis deals with the study of stochastic processes and their ergodicity properties. The
variety of problems encountered calls for a set of different approaches, ranging from …