Minimization of inhomogeneous biharmonic eigenvalue problems
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Publication:2294786
DOI10.1016/j.apm.2017.07.015zbMath1480.49046OpenAlexW2736152558MaRDI QIDQ2294786
Publication date: 12 February 2020
Published in: Applied Mathematical Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apm.2017.07.015
Boundary value problems for higher-order elliptic equations (35J40) Vibrations in dynamical problems in solid mechanics (74H45) Estimates of eigenvalues in context of PDEs (35P15) Variational methods for eigenvalues of operators (49R05)
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Cites Work
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- Maximization of the first eigenvalue in problems involving the bi-Laplacian
- Optimality conditions for the buckling of a clamped plate
- The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization
- Bounds for the eigenvalues of some vibrating systems
- Some results on the frequencies of nonhomogeneous rods
- Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
- On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle
- On the fundamental eigenfunctions of a clamped punctured disk
- High precision solutions of two fourth order eigenvalue problems
- Rayleigh's conjecture on the principal frequency of the clamped plate
- On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions
- A numerical existence proof of nodal lines for the first eigenfunction of the plate equation
- Efficient rearrangement algorithms for shape optimization on elliptic eigenvalue problems
- Extremal principal eigenvalue of the bi-Laplacian operator
- A few shape optimization results for a biharmonic Steklov problem
- Minimizing eigenvalues for inhomogeneous rods and plates
- Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator
- Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates
- Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems
- Minimization of the Ground State for Two Phase Conductors in Low Contrast Regime
- On the Optimal Design of Columns Against Buckling
- Convex shape optimization for the least biharmonic Steklov eigenvalue
- Vibrations of thin plates with small clamped patches
- Global minimizer of the ground state for two phase conductors in low contrast regime
- The free vibration of rectangular plates
- Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes
- Asymptotics of eigenvalues of a plate with small clamped zone
