5 citations · 12 across the 8 of their papers we have counts for
11 papers · 1 filter
Gehring's Lemma for kinetic Fokker-Planck equations
Jessica Guerand, Cyril Imbert, Clément Mouhot
In this article, we establish a "Gehring lemma" for a real function satisfying a reverse Hölder inequality on all "kinetic cylinders" contained in a large one: it asserts that the…
Regularity and trend to equilibrium for a non-local advection-diffusion model of active particles
Luca Alasio, Jessica Guerand, Simon Schulz
We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this eq…
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +3
We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörm…
A moment-based approach for the analysis of the infinitesimal model in the regime of small variance
J Guerand, M Hillairet, S Mirrahimi
We provide an asymptotic analysis of a nonlinear integro-differential equation describing the evolutionary dynamics of a population which reproduces sexually and which is subject t…
Global smooth solutions for triangular reaction-cross diffusion systems
Jessica Guerand, Angeliki Menegaki, Ariane Trescases
For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smo…
Quantitative De Giorgi methods in kinetic theory
Jessica Guerand, Clément Mouhot
We consider hypoelliptic equations of kinetic Fokker-Planck type, also known as Kolmogorov or ultraparabolic equations, with rough coefficients in the drift-diffusion operator. We…
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…
Quantitative regularity for parabolic De Giorgi classes
Jessica Guerand
We consider Parabolic De Giorgi classes for which we give a fully quantitative proof of the H\''older continuity for functions in these classes using the De Giorgi method. The main…
Classification of nonlinear boundary conditions for 1D nonconvex Hamilton-Jacobi equations
Jessica Guerand
We study Hamilton-Jacobi equations in [0, +) of evolution type with nonlinear boundary conditions of Neumann type in the case where the Hamiltonian is non necessarily conve…
Flux-limited solutions and state constraints for quasi-convex Hamilton-Jacobi equations
Jessica Guerand
Imbert and Monneau proved that Soner's formulation of state constraint problems on a bounded interval is equivalent to the so-called flux-limited formulation they introduced recent…
Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction
Jessica Guerand, Marwa Koumaiha
This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes r…