Lotoreichik, VladimirVladimirLotoreichikRohleder, JonathanJonathanRohleder2019-11-272019-11-272017-07-05Journal of Differential Equations 1 (263): 491-508 (2017-07-05)http://hdl.handle.net/11420/3897Inequalities 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.en0022-039620171491508Eigenvalue inequalityLaplace operatorLipschitz domainMixed boundary conditionsPolyhedral domainJournal Article10.1016/j.jde.2017.02.043Other