  We consider an eigenvalue problem for the biharmonic operator with
Steklov-type boundary conditions. We obtain it as a limiting Neumann problem
for the biharmonic operator in a process of mass concentration at the boundary.
We study the dependence of the spectrum upon the domain. We show analyticity of
the symmetric functions of the eigenvalues under isovolumetric perturbations
and prove that balls are critical points for such functions under measure
constraint. Moreover, we show that the ball is a maximizer for the first
positive eigenvalue among those domains with a prescribed fixed measure.
