Estimates for eigenvalues of the Neumann and Steklov problems
Feng Du, Jing Mao, Qiaoling Wang, Changyu Xia, Yan Da Zhao · Advances in Nonlinear Analysis · 2023
Abstract We prove Li-Yau-Kröger-type bounds for Neumann-type eigenvalues 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.