Estimates for eigenvalues of the Neumann and Steklov problems

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.

Keywords

• neumann eigenvalue problem
• steklov eigenvalue problem
• biharmonic operator
• eigenvalues
• fourier transform
• 35p15
• 53c40
• 58c40