On the first eigenvalue of a fourth order Steklov problem

DOI10.1007/s00526-008-0199-9zbMath1171.35089OpenAlexW2034937639MaRDI QIDQ1016342

Dorin Bucur, Alberto Ferrero, Gazzola, Filippo

Publication date: 5 May 2009

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-008-0199-9

zbMATH Keywords

eigenvalue problembiharmonic equationdisprove a long-standing conjectureFichera's principle of dualityfourth order Steklov problem

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (28)

Optimality conditions of the first eigenvalue of a fourth order Steklov problem ⋮ Nyström methods and extrapolation for solving Steklov eigensolutions and its application in elasticity ⋮ On a Classical Spectral Optimization Problem in Linear Elasticity ⋮ Conforming finite element approximations for a fourth-order Steklov eigenvalue problem ⋮ The S.V.D. of the Poisson kernel ⋮ Estimate for the first fourth Steklov eigenvalue of a minimal hypersurface with free boundary ⋮ Bulk-boundary eigenvalues for bilaplacian problems ⋮ The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization ⋮ Sharp bounds for the first eigenvalue of a fourth-order Steklov problem ⋮ A note on Kuttler-Sigillito's inequalities ⋮ Spectral stability for a class of fourth order Steklov problems under domain perturbations ⋮ Positivity for fourth-order semilinear problems related to the Kirchhoff-love functional ⋮ A virtual element method for a biharmonic Steklov eigenvalue problem ⋮ Hardy-Rellich inequalities with boundary remainder terms and applications ⋮ On the Eigenvalues of a Biharmonic Steklov Problem ⋮ On asymptotic properties of biharmonic Steklov eigenvalues ⋮ On some higher order Hardy-Rellich type inequalities with boundary terms ⋮ Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator ⋮ 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 ⋮ On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: well-posedness, regularity theory and eigenvalue problems ⋮ A sharp isoperimetric inequality for the second eigenvalue of the Robin plate ⋮ A novel numerical method based on a high order polynomial approximation of the fourth order Steklov equation and its eigenvalue problems ⋮ An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem ⋮ A few shape optimization results for a biharmonic Steklov problem ⋮ The Bilaplacian with Robin Boundary Conditions ⋮ Shape deformation for vibrating hinged plates ⋮ Two inequalities for the first Robin eigenvalue of the Finsler Laplacian ⋮ On the spectra of three Steklov eigenvalue problems on warped product manifolds

Cites Work

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