Extremal principal eigenvalue of the bi-Laplacian operator

Abstract In this paper we propose two numerical algorithms to derive the extremal principal eigenvalue of the bi-Laplacian operator under Navier boundary conditions or Dirichlet boundary conditions. Consider a non-homogeneous hinged or clamped plate Ω , the algorithms converge to the density functions on Ω which yield the maximum or minimum basic frequency of the plate.

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