Reverse Hardy-Littlewood-Sobolev inequalities

José Carrillo (1) , Matías G Delgadino (1) , Jean Dolbeault (2) , Rupert L Frank (3) , Franca Hoffmann (4)

1 Department of Mathematics [Imperial College London]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Mathematisches Institut, Ludwig-Maximilians Universität München
4 Department of Computing and Mathematical sciences

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.

Domaines: Equations aux dérivées partielles [math.AP]

José Carrillo, Matías G Delgadino, Jean Dolbeault, Rupert L Frank, Franca Hoffmann. Reverse Hardy-Littlewood-Sobolev inequalities. 2018. ⟨hal-01837888v1⟩