Lusin approximation for horizontal curves in step 2 Carnot groups

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• 作者：Enrico Le Donne…
• 关键词：Mathematics Subject Classification28C15 ; 49Q15 ; 43A80
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：55
• 期：5
• 全文大小：525 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835
• 卷排序：55

文摘

A Carnot group \(\mathbb {G}\) admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve \(\gamma \) in \(\mathbb {G}\) and \(\varepsilon >0\), there is a \(C^1\) horizontal curve \(\Gamma \) such that \(\Gamma =\gamma \) and \(\Gamma '=\gamma '\) outside a set of measure at most \(\varepsilon \). We verify this property for free Carnot groups of step 2 and show that it is preserved by images of Lie group homomorphisms preserving the horizontal layer. Consequently, all step 2 Carnot groups admit Lusin approximation for horizontal curves.