Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator
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Publication:2832789
DOI10.1007/978-3-319-41538-3_5zbMath1349.35254arXiv1603.02923OpenAlexW2295469066MaRDI QIDQ2832789
Publication date: 14 November 2016
Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.02923
eigenvaluesboundary value problemsperturbationsbiharmonic operatorplatesSteklovisovolumetric perturbationsHadamard formulasshape criticality
Related Items (12)
On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate ⋮ Neumann eigenvalues of the biharmonic operator on domains: geometric bounds and related results ⋮ Spectral Optimization of Inhomogeneous Plates ⋮ Estimates for eigenvalues of the Neumann and Steklov problems ⋮ Minimization of the buckling load of a clamped plate with perimeter constraint ⋮ Bulk-boundary eigenvalues for bilaplacian problems ⋮ Domain perturbation for the solution of a periodic Dirichlet problem ⋮ Semiclassical bounds for spectra of biharmonic operators ⋮ Minimization of inhomogeneous biharmonic eigenvalue problems ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ On the explicit representation of the trace space \(H^{\frac{3}{2}}\) and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems ⋮ The Bilaplacian with Robin Boundary Conditions
Cites Work
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- Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators
- An isoperimetric inequality for fundamental tones of free plates
- The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization
- Positivity preserving property for a class of biharmonic elliptic problems
- Spectral stability of general non-negative selfadjoint operators with applications to Neumann-type operators
- A real analyticity result for symmetric functions of the eigenvalues of a domain-dependent Neumann problem for the Laplace operator
- Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
- On the first eigenvalue of a fourth order Steklov problem
- Spectral stability of the Neumann Laplacian.
- 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 few shape optimization results for a biharmonic Steklov problem
- The biharmonic Neumann problem in Lipschitz domains
- Inequalities for membrane and Stekloff eigenvalues
- Shape deformation for vibrating hinged plates
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
- A survey on boundary conditions for the biharmonic
- A new system of boundary integral equations for plates with free edges
- Convex shape optimization for the least biharmonic Steklov eigenvalue
- On the Positivity Preserving Property of Hinged Plates
- Shape Sensitivity Analysis of the Eigenvalues of the Reissner--Mindlin System
- Eigenvalues of polyharmonic operators on variable domains
- Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems
- Remarks on a Stekloff Eigenvalue Problem
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