Optimization of the first eigenvalue in problems involving the bi-Laplacian

CUCCU, FABRIZIO;PORRU G.

2009-01-01

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Abstract

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 Ω which is clamped along the boundary. Given several materials (with different densities) of total extension |Ω| , we investigate the location of these materials throughout Ω so to minimize or maximize the first eigenvalue in the vibration of the clamped plate.