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Zbl 1181.35154
Cuccu, Fabrizio; Porru, Giovanni
Optimization of the first eigenvalue in problems involving the bi-Laplacian. (English)
[J] Differ. Equ. Appl. 1, No. 2, Article ID 12, 219-235 (2009). ISSN 1847-120X

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

MSC 2000:: *35P15 Estimation of eigenvalues for PD operators
47A75 Eigenvalue problems (linear operators)
74K20 Plates
74P10 Optimization of other properties
49K20 Optimal control problems with PDE (nec./ suff.)

Keywords: bi-Laplacian; eigenvalues; minimization; maximization; rearrangements

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