Journal des Mathematiques Pures et Appliquees
© 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.
Submitted to ORA
01 Dec 2019