Young Researchers Workshop: Kinetic descriptions in theory and applications

Reverse Hardy-Littlewood-Sobolev inequalities

Franca Hoffmann

California Institute of Technology
[SLIDES]

We will introduce a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with free energy functionals and nonlinear diffusion equations involving mean field drifts. This is joint work with José A. Carrillo, Matias G. Delgadino, Jean Dolbeault, and Rupert L. Frank.