2.3k citations · 4k across the 36 of their papers we have counts for
49 papers
Conditional estimates for the non-cutoff Boltzmann equation in a bounded domain
Zhimeng Ouyang, Luis Silvestre
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular…
Entropy dissipation estimates for the Boltzmann equation without cut-off
Jamil Chaker, Luis Silvestre
We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted -Norm. The estimate holds for a wide range of potentials including so…
Holder estimates for kinetic Fokker-Planck equations up to the boundary
Luis Silvestre
We obtain local Holder continuity estimates up to the boundary for a kinetic Fokker-Planck equation with rough coefficients, with the prescribed influx boundary condition. Our resu…
Regularity estimates and open problems in kinetic equations
Luis Silvestre
We survey some new results regarding a priori regularity estimates for the Boltzmann and Landau equations conditional to the boundedness of the associated macroscopic quantities. W…
Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian
Luis Silvestre, Stanley Snelson
The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence…
Singular solutions to parabolic equations in nondivergence form
Luis Silvestre
For any , we construct an example of a solution to a parabolic equation with measurable coefficients in two space dimensions which has an isolated singularity and is no…