Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet Laplace eigenvalues on integer lattices

Bobo Hua School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China Yong Lin Department of Mathematics, Information School, Renmin University of China, Beijing 100872, China Yanhui Su College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China

Differential Geometry mathscidoc:2207.10007

arXiv, 2017.10
In this paper, we prove some analogues of Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice $\Z^n.$ This partially answers a question posed by Chung and Oden.
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@inproceedings{bobo2017payne-polya-weinberger,,
  title={Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet Laplace eigenvalues on integer lattices},
  author={Bobo Hua, Yong Lin, and Yanhui Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707160359853525577},
  booktitle={arXiv},
  year={2017},
}
Bobo Hua, Yong Lin, and Yanhui Su. Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet Laplace eigenvalues on integer lattices. 2017. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707160359853525577.
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