138 citations · 208 across the 12 of their papers we have counts for
8 papers · 1 filter
Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
We provide a scheme of a recent stability result for a family of Gagliardo-Nirenberg-Sobolev (GNS) inequalities, which is equivalent to an improved entropy - entropy production ine…
Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
The purpose of this work is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates bet…
Stability in Gagliardo-Nirenberg inequalities - Supplementary material
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret +1
This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or eleme…
Weighted fast diffusion equations (Part I): Sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities
Matteo Bonforte, Jean Dolbeault, Matteo Muratori +1
In this paper we consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities (CKN), with two radial power law weights and exponents in a subcritical range. We address…
Weighted fast diffusion equations (Part II): Sharp asymptotic rates of convergence in relative error by entropy methods
Matteo Bonforte, Jean Dolbeault, Matteo Muratori +1
This paper is the second part of the study. In Part~I, self-similar solutions of a weighted fast diffusion equation (WFD) were related to optimal functions in a family of subcritic…
Weighted interpolation inequalities: a perturbation approach
Jean Dolbeault, Matteo Muratori, Bruno Nazaret
We study optimal functions in a family of Caffarelli-Kohn-Nirenberg inequalities with a power-law weight, in a regime for which standard symmetrization techniques fail. We establis…
From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach
Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré
We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Function…
On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré
The goal of this paper is to give a non-local sufficient condition for generalized Poincaré inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poinc…