370 citations · 902 across the 32 of their papers we have counts for
40 papers
Local regularity for the space-homogeneous Landau equation with very soft potentials
François Golse, Cyril Imbert, Sehyun Ji +1
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix…
Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations
Jessica Guerand, Cyril Imbert
This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering…
Regularity for the Boltzmann equation conditional to macroscopic bounds
Cyril Imbert, Luis Silvestre
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global…
Regularity of solutions of a fractional porous medium equation
Cyril Imbert, Rana Tarhini, François Vigneron
This article is concerned with a porous medium equation whose pressure law is both nonlinear and nonlocal, namely $\partial_t u = { \nabla \cdot} \left(u \nabla(-Δ)^{\fracα{2}-1}u^…
Global regularity estimates for the Boltzmann equation without cut-off
Cyril Imbert, Luis Silvestre
We derive a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy de…
Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb Potential
François Golse, Maria Pia Gualdani, Cyril Imbert +1
We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal.…