A note on the Neumann eigenvalues of the biharmonic operator

We study the dependence of the eigenvalues of the biharmonic operator subject to Neumann boundary conditions on the Poisson's ratio sigma. In particular, we prove that the Neumann eigenvalues are Lipschitz continuous with respect to sigma[0,1[and that all the Neumann eigenvalues tend to zero as sigma 1(-). Moreover, we show that the Neumann problem defined by setting sigma = 1 admits a sequence of positive eigenvalues of finite multiplicity that are not limiting points for the Neumann eigenvalues with sigma[0,1[as sigma 1(-) and that coincide with the Dirichlet eigenvalues of the biharmonic operator. Copyright (c) 2016 John Wiley & Sons, Ltd.