Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants

Dolbeault, Jean; Esteban, Maria J.

Dolbeault, Jean; Esteban, Maria J. (2011), Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants, in Exner, Pavel, Mathematical results in quantum physics. Proceedings of the QMath11 Conference Hradec Králové, Czech Republic, 6 - 10 September 2010, World Scientific, p. 178-182. http://dx.doi.org/10.1142/9789814350365_0017

Type

Communication / Conférence

External document link

http://arxiv.org/abs/1009.5619v1

Date

2011

Conference title

Conference on mathematical results in quantum physics (QMATH-11)

Conference date

2010-09

Conference city

Hradec Králové

Conference country

République tchèque

Book title

Mathematical results in quantum physics. Proceedings of the QMath11 Conference Hradec Králové, Czech Republic, 6 - 10 September 2010

Book author

Exner, Pavel

Publisher

World Scientific

Pages

178-182

Abstract (EN)

This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers [1–5] in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint.

Subjects / Keywords

Caffarelli-Kohn-Nirenberg inequality; Gagliardo-Nirenberg inequality; logarithmic Hardy inequality; logarithmic Sobolev inequality; extremal functions; radial symmetry; symmetry breaking; Emden-Fowler transformation; linearization; existence; compactness; optimal constants