Sharp Differentiability Results for the Lower Local Lipschitz Constant and Applications to Non-embedding

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• 作者：K. Wildrick ; T. Zürcher
• 关键词：Differentiability ; Poincaré inequality ; Lorentz space ; Sobolev space ; Embedding ; 26B05 ; 30L05
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：25
• 期：4
• 页码：2590-2616
• 全文大小：608 KB
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• 作者单位：K. Wildrick (1)
  T. Zürcher (2)
  
  1. Département de mathématiques, Université de Fribourg, Chemin du Musée 23, 1700, Fribourg, Switzerland
  2. Jyv?skyl?n yliopisto, Matematiikan ja tilastotieteen laitos, PL 35 (MaD), 40014, Jyv?skyl?, Finland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincaré inequality to a Banach space with the Radon–Nikodym property that guarantees differentiability at almost every point. We apply these results to obtain a non-embedding theorem for a corresponding class of mappings. Keywords Differentiability Poincaré inequality Lorentz space Sobolev space Embedding