138 citations · 208 across the 12 of their papers we have counts for
13 papers
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…
Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
Nazaret Bruno, Mohammed Bachir, Bruno Nazaret
Schweizer, Sklar and Thorp proved in 1960 that a Menger space under a continuous -norm , induce a natural topology wich is metrizable. We extend this result to…
Infinite-horizon problems under periodicity constraint
Joel Blot, Abdelkader Bouadi, Bruno Nazaret
We study so{ù}e infinite-horizon optimization problems on spaces of periodic functions for non periodic Lagrangians. The main strategy relies on the reduction to finite horizon tha…
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…
Geodesics for a class of distances in the space of probability measures
Pierre Cardaliaguet, Guillaume Carlier, Bruno Nazaret
In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the exi…
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…
A new class of transport distances
Jean Dolbeault, Bruno Nazaret, Giuseppe Savare
We introduce a new class of distances between nonnegative Radon measures in Euclidean spaces. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasse…
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…
Optimal transportation for the determinant
Guillaume Carlier, Bruno Nazaret
Among -valued triples of random vectors having fixed marginal probability laws, what is the best way to jointly draw in such a way that the simplex genera…