Optimization of the first eigenvalue in problems involving the bi-Laplacian
Fabrizio Cuccu, Giovanni Porru · Differential Equations & Applications · 2009
This paper concerns minimization and maximization of the first eigenvalue in problems involving the bi-Laplacian under Dirichlet boundary conditions. Physically, in case of N = 2 , our equation models the vibration of a non homogeneous plate which is clamped along the boundary. Given several materials (with different densities) of total extension || , we investigate the location of these materials throughout so to minimize or maximize the first eigenvalue in the vibration of the clamped plate.