Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

Jean Dolbeault (), Maria J. Esteban (), Michal Kowalczyk () and Michael Loss ()
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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

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 225-242 from Springer

Abstract: 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; 26D10; 46E35; 58E35 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-41401-5_9

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DOI: 10.1007/978-3-642-41401-5_9

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