Speaker  Introduction

Maria Gualdani is an Associate Professor at George Washington University. Her research interest is in applied partial differential equations, including kinetic theory and mean field games.

Maria Gualdani received her BS degree in 2000 at the University of Florence (Italy) and her PhD in 2005 at the Johannes Gutenberg University (Germany). Her PhD advisor was Ansgar Jüngel. 

She is the recipient of several awards, including the George Washington University Early Career Researcher Award (2016) and the NSF Career Award (2017). Currently she holds a Research Chair at George Washington University. 

Title   On Ap Weights and Regularization for the Homogeneous Landau Equation

Abstract

In this course we present the homogeneous Landau equation and show that for moderately soft potentials there is a regularization effect with estimates determined only by the mass, energy and entropy. For general potentials, it is shown that a similar regularization takes place provided an additional condition is satisfied uniformly over time. This condition, which may be described as a nonlinear Morrey space bound, always holds for moderately soft potentials, and nearly holds for general potentials, including Coulomb. The main feature of the proofs is the analysis of the Landau operator  as a Schroedinger operator whose coefficients are Ap-weights. This is a joint work with Nestor Guillen.