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Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • Jean Dolbeault

    (Université Paris-Dauphine, Ceremade)

  • Maria J. Esteban

    (Université Paris-Dauphine, Ceremade)

  • Michal Kowalczyk

    (Universidad de Chile, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS))

  • Michael Loss

    (Georgia Institute of Technology)

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.

Suggested Citation

  • Jean Dolbeault & Maria J. Esteban & Michal Kowalczyk & Michael Loss, 2014. "Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 225-242, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_9
    DOI: 10.1007/978-3-642-41401-5_9
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