Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

Dolbeault, Jean; Esteban, Maria J.; Kowalczyk, Michal; Loss, Michael

Dolbeault, Jean; Esteban, Maria J.; Kowalczyk, Michal; Loss, Michael (2014), Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences, in Ciarlet, Philippe G.; Li, Tatsien; Maday, Yvon, Partial Differential Equations: Theory, Control and Approximation. In Honor of the Scientific Heritage of Jacques-Louis Lions, Springer : Berlin, p. 225-242. http://dx.doi.org/10.1007/978-3-642-41401-5_9

Type

Chapitre d'ouvrage

External document link

http://hal.archives-ouvertes.fr/hal-00739140

Date

2014

Book title

Partial Differential Equations: Theory, Control and Approximation. In Honor of the Scientific Heritage of Jacques-Louis Lions

Book author

Ciarlet, Philippe G.; Li, Tatsien; Maday, Yvon

Publisher

Springer

Published in

Berlin

ISBN

978-3-642-41400-8

Number of pages

429

Pages

225-242

Abstract (EN)

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.

Subjects / Keywords

Inequality; Interpolation; Gagliardo-Nirenberg inequality; Logarithmic Sobolev inequality; Heat equation