Reverse Hardy-Littlewood-Sobolev inequalities

Carrillo, Jose A.; Delgadino, Matias G.; Dolbeault, Jean; Frank, Rupert L. and Hoffmann, Franca (2019): Reverse Hardy-Littlewood-Sobolev inequalities. In: Journal De Mathematiques Pures et Appliquees, Vol. 132: pp. 133-165

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0021-7824
• Language: English