Minimization of eigenvalues and construction of non-degenerate potentials for the one-dimensional p-Laplacian

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• 作者：ZhiYuan Wen ; MeiRong Zhang
• 关键词：p ; Laplacian ; eigenvalue ; minimization problem ; Schwarz rearrangement ; non ; degenerate potential ; boundary value problem ; 34L15 ; 49R05 ; 34L40 ; 49J15 ; 34B05
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：59
• 期：1
• 页码：49-66
• 全文大小：262 KB
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• 作者单位：ZhiYuan Wen (1)
  MeiRong Zhang (1)
  
  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of non-degenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations. Keywords p-Laplacian eigenvalue minimization problem Schwarz rearrangement non-degenerate potential boundary value problem