Eigenvalue inequalities for mixed Steklov problems

2009/09/30 by R. Banuelos, Banuelos, R., T. Kulczycki +5 · 1 citation
Computer Science · Engineering · Mathematics · #35P15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P15

paper · pdf · doi:10.48550/arxiv.0909.5473

Major revision

openalex publication_date 2009/09/30 · arxiv created 2010/03/02 · arxiv updated 2010/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend some classical inequalities between the Dirichlet and Neumann eigenvalues of the Laplacian to the context of mixed Steklov--Dirichlet and Steklov--Neumann eigenvalue problems. The latter one is also known as the sloshing problem, and has been actively studied for more than a century due to its importance in hydrodynamics. The main results of the paper are applied to obtain certain geometric information about nodal sets of sloshing eigenfunctions. The key ideas of the proofs include domain monotonicity for eigenvalues of mixed Steklov problems, as well as an adaptation of Filonov's method developed originally to compare the Dirichlet and Neumann eigenvalues.

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• Extremal Steklov-Neumann Eigenvalues

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