Abstract
This paper concerns minimization and maximization of the energy integral 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 equilibrium configuration of a non-homogeneous plate Ω which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension |Ω|, we investigate the location of these materials inside Ω so to maximize or minimize the energy integral of the corresponding plate.
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Anedda, C. Maximization and minimization in problems involving the bi-Laplacian. Annali di Matematica 190, 145–156 (2011). https://doi.org/10.1007/s10231-010-0142-5
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DOI: https://doi.org/10.1007/s10231-010-0142-5