1 citations · 3 across the 10 of their papers we have counts for
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Döblin--Fourier cancellation and kinetic Aleksandrov estimates
Amélie Loher, Connor Mooney, Clément Mouhot
We develop a cancellation mechanism for linear second-order kinetic equations in non-divergence form with measurable uniformly elliptic coefficients. We decompose the dynamics into…
Homogenization at a polynomial scale in high contrast
Scott Armstrong, Tuomo Kuusi, Amélie Loher
We prove an upper bound on the homogenization length scale which is a fixed power of the coarse ellipticity ratio for coefficient fields that satisfy a finite range of dependence a…
Conditional appearance of decay for the non-cutoff Boltzmann equation in a bounded domain
Cyril Imbert, Amélie Loher
This work is concerned with the generation of decay estimates in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff on a bounded spati…
Production of the Fisher information for the Landau-Coulomb equation with L1 initial data
Laurent Desvillettes, William Golding, Maria Pia Gualdani +1
We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded…
Semi-local behaviour of non-local hypoelliptic equations: Boltzmann
Amélie Loher
The purpose of this note is to demonstrate the announced result in [Loher, The Strong Harnack inequality for the Boltzmann equation, Séminaire Laurent Schwartz proceeding] by filli…
Semi-local behaviour of non-local hypoelliptic equations: divergence form
Amélie Loher
We derive the Strong Harnack inequality for a class of hypoelliptic integro-differential equations in divergence form. Our result is semi-local, in the sense that we require the 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…
Global smooth solutions to the Landau-Coulomb equation in
William Golding, Maria Gualdani, Amélie Loher
We consider the homogeneous Landau equation in with Coulomb potential and initial data in polynomially weighted . We show that there exists a smooth solutio…
Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with initial datum
William Golding, Amélie Loher
We consider the homogeneous Landau equation with Coulomb potential and general initial data , where is arbitrarily close to . We show the local-in-time exi…
Quantitative Schauder estimates for hypoelliptic equations
Amélie Loher
We derive Schauder estimates using ideas from Campanato's approach for a general class of local hypoelliptic operators and non-local kinetic equations. The method covers equations…
Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium
William Golding, Maria Gualdani, Amélie Loher
We consider the Landau equation with Coulomb potential in the spatially homogeneous case. We show short time propagation of smallness in norms for and instantaneous r…
Quantitative De Giorgi methods in kinetic theory for non-local operators
Amélie Loher
We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a ter…