| A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN |
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| 引用本文： | Ren Xin′an Xu HongweiCenter of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China.. A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN[J]. 高校应用数学学报(英文版), 2004, 0(2) |
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| 作者姓名： | Ren Xin′an Xu HongweiCenter of Mathematical Sciences Zhejiang University Hangzhou 310027 China. |
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| 作者单位： | Ren Xin′an Xu HongweiCenter of Mathematical Sciences，Zhejiang University，Hangzhou 310027，China. |
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| 基金项目： | Research supported by the National Natural Science Foundation of China( 1 0 2 31 0 1 0 )，Trans- CenturyTraining Programme Foundation for Talents by the Ministry of Education of China，Natural ScienceFoundation of Zhejiang provinc |
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| 摘 要： | §1 IntroductionLet( Mn,ds2 ) be an n-dimensional connected compact Riemannian manifold with orwithout boundary.In local coordinates( x1 ,...,xn) ,the Riemannian metric is given byds2 =∑gijdxidxjand the Laplace-Beltrami operatorΔacting on function is defined asΔ=g- 1 / 2 ∑ xi g1 / 2 gij xj ,where( gij) =( gij) - 1 and g=det( gij) .Set N = M.Let f be a smooth function on M,we consider the following eigenvalueproblems.( A) ( i) When N= ,i.e.,M is closed,we consider the free membrane…
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A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN |
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| Abstract: | |
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| Keywords: | Riemannian manifold Laplace-Beltrami operator eigenvalue mixed boundary condition. |
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