A note on the area and coarea formulas for general volume densities and some applications

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• 作者：Daniel Cibotaru ; Jorge de Lira
• 关键词：Primary 58C35 ; 49Q15 ; Secondary 46T12
• 刊名：manuscripta mathematica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：149
• 期：3-4
• 页码：471-506
• 全文大小：621 KB
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• 作者单位：Daniel Cibotaru (1)
  Jorge de Lira (1)
  
  1. Universidade Federal do Ceará, Fortaleza, CE, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. We apply these formulas to derive an anisotropic tube formula for hypersurfaces in \({{\mathbb{R}}^n}\) and to give a short euclidean proof of the anisotropic Sobolev inequality. A discussion about the first variation of the anisotropic area is also included. Mathematics Subject Classification Primary 58C35 49Q15 Secondary 46T12