Reverse Hardy-Littlewood-Sobolev inequalities

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

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0021-7824
• Sprache: Englisch