English

Estimates for eigenvalues of the Neumann and Steklov problems

Differential Geometry 2021-08-03 v2

Abstract

We prove Li-Yau-Kr\"oger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which directly implies two sharp Reilly-type inequalities for the corresponding first nonzero eigenvalue.

Keywords

Cite

@article{arxiv.1902.08998,
  title  = {Estimates for eigenvalues of the Neumann and Steklov problems},
  author = {Feng Du and Jing Mao and Qiaoling Wang and Changyu Xia and Yan Zhao},
  journal= {arXiv preprint arXiv:1902.08998},
  year   = {2021}
}

Comments

18 pages. We have made revisions to v1 based on some useful suggestions from colleagues. Comments are welcome

R2 v1 2026-06-23T07:49:20.586Z