Eigenvalue inequalities for mixed Steklov problems

Autor:	Banuelos, R., Kulczycki, T., Polterovich, I., Siudeja, B.
Rok vydání:	2009
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs 35P15
Druh dokumentu:	Working Paper
Popis:	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. Comment: Major revision
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0909.5473 Zobrazit plný text záznamu View this record from Arxiv