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Sharp Interpolation Inequalities on the Sphere:New Methods and Consequences 被引量：1

Sharp Interpolation Inequalities on the Sphere:New Methods and Consequences
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摘要 This paper is devoted to various considerations on a family of sharp interpo- lation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincare, 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.
作者 Jean DOLBEAULT Maria J. ESTEBAN Michal KOWALCZYK Michael LOSS
机构地区 Ceremade Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI Skiles Building
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第1期99-112,共14页 数学年刊（B辑英文版）
基金 Project supported by ANR grants CBDif and NoNAP,the ECOS project (No. C11E07) the Chileanresearch grants Fondecyt (No. 1090103) Fondo Basal CMM Chile,Project Anillo ACT 125 CAPDEand the National Science Foundation (No.DMS 0901304)
关键词 Sobolev inequality INTERPOLATION Gagliardo-Nirenberg inequality Logarithmic Sobolev inequality Heat equation 插值 球体 Sobolev 不等式 夏普 光谱特性 最佳常数 庞加莱
分类号 O178 [理学—基础数学]
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参考文献37

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Chinese Annals of Mathematics,Series B
2013年 第1期

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