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Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Publikationstyp
Journal Article
Date Issued
2017-07-05
Sprache
English
Author(s)
Institut
TORE-URI
Volume
263
Issue
1
Start Page
491
End Page
508
Citation
Journal of Differential Equations 1 (263): 491-508 (2017-07-05)
Publisher DOI
Scopus ID
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.
Subjects
Eigenvalue inequality
Laplace operator
Lipschitz domain
Mixed boundary conditions
Polyhedral domain