On the eigenvalues of the biharmonic operator with pointwise gradient constraint Original Research Article

We study an eigenvalue problem for some fourth order variational inequalities, which result from a pointwise constraint on the gradient of the unknown function uu. We use a nonsmooth variational approach to find existence and multiplicity (under symmetry assumptions) for solutions of the problem. A major issue to be faced is how to exclude tangency between the set of uuʹs satisfying the contraint condition and the L2L2-sphere.