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.
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