Speaker
Description
Gehring’s lemma states that a function satisfying a reverse Hölder inequality on suitable subdomains enjoys improved integrability. Originally introduced by Gehring in connection with open problems in the theory of quasiconformal mappings, this result has since been adapted to the study of higher integrability properties of gradients of solutions to elliptic and parabolic equations.
In this talk, I will present results obtained through different collaborations: with Cyril Imbert and Clément Mouhot for the kinetic Fokker–Planck equation, and with Francesca Anceschi and Teresa Isernia for nonlinear ultraparabolic equations. The first key step consists in establishing a Gehring-type lemma on kinetic and ultraparabolic cylindrical domains. The second step is to derive reverse Hölder inequalities for gradients of solutions using Poincaré-type inequalities, energy estimates, and integrability properties of the solutions.