Minimization of the first eigenvalue in problems involving the bi-laplacian
Claudia Anedda, Fabrizio Cuccu, Giovanni Porru · Revista de Matemática Teoría y Aplicaciones · 2009
This paper concerns the minimization of the first eigenvalue in problems involving the bi-Laplacian under either homogeneous Navier boundary conditions or homogeneous Dirichlet boundary conditions. Physically, in case of N = 2, our equation models the vibration of a non homogeneous plate Ω which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension |Ω|, we investigate the location of these materials inside Ω so to minimize the first mode in the vibration of the corresponding plate.