Maximization of the first eigenvalue in problems involving the bi-Laplacian

DOI10.1016/j.na.2008.11.043zbMath1238.35066OpenAlexW2062537896MaRDI QIDQ419831

Fabrizio Cuccu, Giovanni Porru

Publication date: 20 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.11.043

zbMATH Keywords

eigenvaluesrearrangementsmaximizationbi-Laplacian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (8)

Minimizing eigenvalues for inhomogeneous rods and plates ⋮ Existence of an extremal ground state energy of a nanostructured quantum dot ⋮ Minimization of the First Nonzero Eigenvalue Problem for Two-Phase Conductors with Neumann Boundary Conditions ⋮ Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates ⋮ Extremal rearrangement problems involving Poisson's equation with Robin boundary conditions ⋮ Extremal principal eigenvalue of the bi-Laplacian operator ⋮ Minimization of inhomogeneous biharmonic eigenvalue problems ⋮ On the Stability of a Nonlinear Nonhomogeneous Multiply Hinged Beam

Cites Work

• Extremal eigenvalue problems for composite membranes. I
• Rearrangements and convexity of level sets in PDE
• Variational problems on classes of rearrangements and multiple configurations for steady vortices
• Sign change for the Green function and for the first eigenfunction of equations of clamped-plate type
• Steiner symmetry in the minimization of the first eigenvalue in problems involving the 𝑝-Laplacian
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Optimization problems for an elastic plate
• Optimization of the first eigenvalue in problems involving the 𝑝-Laplacian
• Maximisation and minimisation on classes of rearrangements
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