Eigenvalue inequalities for the Laplacian with mixed boundary conditions

0475670 - ÚJF 2018 RIV US eng J - Journal Article
Lotoreichik, Vladimir - Rohleder, J.
Eigenvalue inequalities for the Laplacian with mixed boundary conditions.
Journal of Differential Equations. Roč. 263, č. 1 (2017), s. 491-508. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.782, year: 2017

nequalities 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 Polya, Payne, Levine and Weinberger, Friedlander, and others.
Permanent Link: http://hdl.handle.net/11104/0272327