Reverse Hardy–Littlewood–Sobolev inequalities

Author: 

Carrillo, J
Delgadino, M
Dolbeault, J
Frank, R
Hoffmann, F

Publication Date: 

1 December 2019

Journal: 

Journal des Mathematiques Pures et Appliquees

Last Updated: 

2020-11-24T15:43:01.06+00:00

Volume: 

132

DOI: 

10.1016/j.matpur.2019.09.001

page: 

133-165

abstract: 

© 2019 This paper is devoted to 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.

Symplectic id: 

1098161

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article