Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

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• 作者：Jean Dolbeault (1)
  Maria J. Esteban (1)
  Michal Kowalczyk (2)
  Michael Loss (3)
  
• 关键词：Sobolev inequality ; Interpolation ; Gagliardo ; Nirenberg inequality ; Logarithmic Sobolev inequality ; Heat equation ; 26D10 ; 46E35 ; 58E35
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2013
• 出版时间：January 2013
• 年：2013
• 卷：34
• 期：1
• 页码：99-112
• 全文大小：279KB
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• 作者单位：Jean Dolbeault (1)
  Maria J. Esteban (1)
  Michal Kowalczyk (2)
  Michael Loss (3)
  
  1. Place de Lattre de Tassigny, Université Paris-Dauphine, 75775, Paris Cédex 16, France
  2. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
  3. Skiles Building, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA
  
• ISSN：1860-6261

文摘

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.