Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems

DOI10.1080/17476933.2011.557155zbMath1287.35048arXiv1101.5930OpenAlexW3099363433MaRDI QIDQ5417834

Pier Domenico Lamberti

Publication date: 22 May 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5930

zbMATH Keywords

Laplace operatordomain perturbationSteklov eigenvaluesoverdetermined systems

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Estimates of eigenvalues in context of PDEs (35P15) Sensitivity analysis for optimization problems on manifolds (49Q12) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Related Items (12)

On Vibrating Thin Membranes with Mass Concentrated Near the Boundary: An Asymptotic Analysis ⋮ PDE problems with concentrating terms near the boundary ⋮ A nonlinear damped transmission problem as limit of wave equations with concentrating nonlinear terms away from the boundary ⋮ Shape perturbation of Grushin eigenvalues ⋮ Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator ⋮ Multiple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach ⋮ On Steklov-Neumann boundary value problems for some quasilinear elliptic equations ⋮ A few shape optimization results for a biharmonic Steklov problem ⋮ The Bilaplacian with Robin Boundary Conditions ⋮ Shape deformation for vibrating hinged plates ⋮ A note on the Sobolev trace inequality ⋮ Steklov-Neumann eigenproblems: a spectral characterization of the Sobolev trace spaces

Cites Work

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• Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems
• Absence of critical mass densities for a vibrating membrane
• Isolation and simplicity for the first eigenvalue of the \(p\)-Laplacian with a nonlinear boundary condition
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Boundary regularity for solutions of degenerate elliptic equations
• An analyticity result for the dependence of multiple eigenvalues and eigenspaces of the laplace operator upon perturbation of the domain
• First Variations of the Best Sobolev Trace Constant with Respect to the Domain

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