5 papers · 1 filter
Introduction to quantitative De Giorgi methods
Giovanni Brigati, Clément Mouhot
The theory of De Giorgi (1958) and Nash (1959) solves Hilbert's 19th problem and constitutes a major advance in the analysis of PDEs in the 20th century. This theory concerns the H…
Critical trajectories in kinetic geometry
Helge Dietert, Clément Mouhot, Lukas Niebel +1
We construct critical trajectories in kinetic geometry, i.e. curves in that are: tangential to the vector fields and , co…
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +5
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…
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…
Quantitative fluid approximation in fractional regimes of transport equations with more invariants
Ãmeric Bouin, Laura Kanzler, Clément Mouhot
We present an extension of results in a previous paper by the first and the last author [PMP, 2022] about macroscopic limits of linear kinetic equations in (potentially) fractional…