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Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

  • Jean Dolbeault
  • Maria J. Esteban
  • Michal Kowalczyk
  • Michael Loss

Abstract

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.

Keywords

Inequality Interpolation Gagliardo-Nirenberg inequality Logarithmic Sobolev inequality Heat equation 

Mathematics Subject Classification

26D10 46E35 58E35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jean Dolbeault
    • 1
  • Maria J. Esteban
    • 1
  • Michal Kowalczyk
    • 2
  • Michael Loss
    • 3
  1. 1.CeremadeUniversité Paris-DauphineParis Cedex 16France
  2. 2.Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS)Universidad de ChileSantiagoChile
  3. 3.Georgia Institute of TechnologyAtlantaUSA

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