| Abstract: |
| Biharmonic eigenvalue problems arise in the study of the mechanical vibration of plates. In this work, we discuss the minimization of the first eigenvalue of clamped plate, simply supported plate, and buckling of a plate. A rearrangement algorithm is proposed to find the optimal coefficient function based on the variational formula of the first eigenvalue. On various domains, such as square, circular and annular domains, the region where the optimal coefficient function takes the larger value may have different topologies. We show how the optimal configurations change with respect to plates with various domains. |
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