On the Cheeger sets in strips and non-convex domains

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• 作者：Gian Paolo Leonardi ; Aldo Pratelli
• 关键词：Cheeger sets ; Prescribed mean curvature ; Isoperimetric ; 49Q10 ; 53A10 ; 35P15
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：55
• 期：1
• 全文大小：844 KB
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• 作者单位：Gian Paolo Leonardi (1)
  Aldo Pratelli (2)
  
  1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/b, 41100, Modena, Italy
  2. Department of Mathematics, University of Erlangen, Cauerstrasse 11, 90158, Erlangen, Germany
  
• 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

文摘

In this paper we consider the Cheeger problem for non-convex domains, with a particular interest in the case of planar strips, which have been extensively studied in recent years. Our main results are an estimate on the Cheeger constant of strips, which is stronger than the previous one known from Krejčiřík and Pratelli (Pac J Math 254(2):309–333, 2011), and the proof that strips share with convex domains a number of crucial properties with respect to the Cheeger problem. Moreover, we present several counterexamples showing that the same properties are not valid for generic non-convex domains. Keywords Cheeger sets Prescribed mean curvature Isoperimetric