Eigenvalue inequalities for mixed Steklov problems

By Rodrigo Bañuelos, Tadeusz Kulczycki, Iosif Polterovich, Bartlomiej Siudeja. 2009

47 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d573b2bfbb84b8a50628f8deb1f8140439179959

Citations in the corpus

• SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “There is an extensive literature on the properties of sloshing eigenvalues and eigenfunctions, see [37, 8, 73] and references therein.”