5 papers · 1 filter
Nonlinear kinetic Fokker-Planck equations as gradient flows of the free energy
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault +1
We consider nonhomogeneous kinetic equations that involve a free transport operator and a diffusion of porous medium type acting on velocities. The main novelty is a gradient flow…
The fundamental solution of a nonlinear kinetic Fokker-Planck equation
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has i…
Monotonicity of the period and positive periodic solutions of a quasilinear equation
Jean Dolbeault, Marta GarcÃa-Huidobro, Raúl Manásevich
We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the -Laplace operator. First, the monotonicity of the…
Logarithmic Sobolev inequalities: a review on stability and instability results; logarithmic uncertainty principle
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions o…
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…