Estimates for eigenvalues of the Neumann and Steklov problems

2019/02/24 by Feng Du, Du, Feng, Jing Mao +7
Computer Science · Mathematics · #35P15 #53C40 #58C40 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1902.08998

openalex publication_date 2019/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Li-Yau-Kröger 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.

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