Minimization of the first eigenvalue in problems involving the bi-laplacian
Minimization of the first eigenvalue in problems involving the bi-laplacian
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DOI：
10.15517/rmta.v16i1.1422
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
C. Anedda;F. Cuccu;G. Porru
中科院分区：
文献类型：
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作者：
C. Anedda;F. Cuccu;G. Porru
本文研究了在齐次Navier边界条件和齐次Dirichlet边界条件下双Laplacian算子问题的第一特征值的极小化问题。在物理上，当N = 2时，我们的方程模拟了沿边界沿着铰接或固支的非均匀板的振动。给定几种材料（具有不同的密度）的总延伸||我们研究了这些材料在内部的位置，以便最小化相应板振动中的第一模式。关键词：双拉普拉斯，第一特征值，最小化。
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 which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension | |, we investigate the location of these materials inside so to minimize the first mode in the vibration of the corresponding plate. Keywords: bi-Laplacian, first eigenvalue, minimization.