141 citations · 781 across the 77 of their papers we have counts for
94 papers
Weighted bounds for kinetic Fokker-Planck equations and hypocoercivity
Émeric Bouin, Jean Dolbeault, Luca Ziviani
We study the long-time behaviour of solutions to kinetic Fokker-Planck equations with power law confinement potentials and local equilibria with fat tails. Without relying on \emph…
Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits
Emeric Bouin, Jean Dolbeault, Antoine Mellet
In this paper, we focus on a new type of non-linear kinetic Fokker-Planck equation where the non-linearity comes from a non-linear diffusion in the velocity variable. The existence…
Symmetry and symmetry breaking in interpolation inequalities for two-dimensional spinors -- Preliminary results
Jean Dolbeault, Rupert L. Frank, Jonte Weixler
On the two-dimensional Euclidean space, we study a spinorial analogue of the Caffarelli-Kohn-Nirenberg inequality involving weighted gradient norms. This (SCKN) inequality is equiv…
The CKN inequality for spinors: symmetry and symmetry breaking
Jean Dolbeault, Maria J. Esteban, Rupert L. Frank +1
This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar funct…
Stability results for Sobolev, logarithmic Sobolev, and related inequalities
Jean Dolbeault
Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but…
A short review on Improvements and stability for some interpolation inequalities
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
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 Sob…