Maximization of the first eigenvalue in problems involving the bi-Laplacian Original Research Article

This paper concerns maximization of the first eigenvalue in problems involving the bi-Laplacian under either Navier boundary conditions or Dirichlet boundary conditions. Physically, in the case of N=2N=2, our equation models the vibration of a nonhomogeneous plate ΩΩ which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension |Ω||Ω|, we investigate the location of these materials throughout ΩΩ so as to maximize the first eigenvalue in the vibration of the corresponding plate.