Publisher DOI: 10.1016/j.jde.2017.02.043
Title: Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Language: English
Authors: Lotoreichik, Vladimir 
Rohleder, Jonathan 
Keywords: Eigenvalue inequality; Laplace operator; Lipschitz domain; Mixed boundary conditions; Polyhedral domain
Issue Date: 5-Jul-2017
Source: Journal of Differential Equations 1 (263): 491-508 (2017-07-05)
Abstract (english): 
Inequalities for the eigenvalues of the (negative) Laplacian subject to mixed boundary conditions on polyhedral and more general bounded domains are established. The eigenvalues subject to a Dirichlet boundary condition on a part of the boundary and a Neumann boundary condition on the remainder of the boundary are estimated in terms of either Dirichlet or Neumann eigenvalues. The results complement several classical inequalities between Dirichlet and Neumann eigenvalues due to Pólya, Payne, Levine and Weinberger, Friedlander, and others.
URI: http://hdl.handle.net/11420/3897
ISSN: 0022-0396
Journal: Journal of differential equations 
Institute: Mathematik E-10 
Document Type: Article
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