Luis Silvestre

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20232026

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math.AP2026

The entropy production is not always monotone for hard spheres or for Maxwell molecules

Luis Silvestre

In 1966, McKean asked whether the entropy production of the Boltzmann equation must be monotone decreasing in time. We show that this is not the case even in the space-homogeneous…

math.AP2026

The entropy production is not always monotone in the space-homogeneous Boltzmann equation

Luis Silvestre

We show an example of a function and a collision kernel for which the entropy production increases in time when we flow it by the space-homogeneous Boltzmann equation. The collisio…

math.AP2025

$C^{1 + α}$ regularity for fractional $p$ -harmonic functions

Davide Giovagnoli, David Jesus, Luis Silvestre

We establish interior $C^{1, α}$ regularity estimates for some $α > 0$ , for solutions of the fractional $p$ -Laplace equation $(- Δ_{p})^{s} u = 0$ when $p$ is in the range $p \in [2,2/(1-…

math.AP2025

The Landau equation and Fisher information

Nestor Guillen, Luis Silvestre

In this expository note (submitted to Notices of the AMS) we present the ideas used in our recent work ruling out blow up for the Landau equation with Coulomb potential. Blow up is…

math.AP2023

The Landau equation does not blow up

Nestor Guillen, Luis Silvestre

We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in tim…

The entropy production is not always monotone for hard spheres or for Maxwell molecules

The entropy production is not always monotone in the space-homogeneous Boltzmann equation

C1+α regularity for fractional p-harmonic functions

The Landau equation and Fisher information

The Landau equation does not blow up

$C^{1 + α}$ regularity for fractional $p$ -harmonic functions