From the 1 of 5 linked papers with an AI index.
5 papers
The CKN inequality for spinors: symmetry and symmetry breaking
Jean Dolbeault, Maria J. Esteban, Rupert L. Frank +1
The paper studies weighted Sobolev interpolation inequalities for spinor fields, examining when optimal spinors are symmetric and when symmetry breaks, using spectral analysis tech…
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…
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…
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…
Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
We prove a sharp quantitative version for the stability of the Sobolev inequality with explicit constants. Moreover, the constants have the correct behavior in the limit of large d…