On an Isoperimetric Inequality for the First Eigenvalue of a Boundary Value Problem

DOI10.1137/0508020zbMath0359.35060OpenAlexW1997926038MaRDI QIDQ4132928

Miriam Bareket

Publication date: 1977

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0508020

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Inequalities and extremum problems involving convexity in convex geometry (52A40)

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PDE comparison principles for Robin problems ⋮ On the maximal mean curvature of a smooth surface ⋮ An optimization problem for finite point interaction families ⋮ An estimate for the anisotropic maximum curvature in the planar case ⋮ Bounds and extremal domains for Robin eigenvalues with negative boundary parameter ⋮ Optimisation of the lowest Robin eigenvalue in the exterior of a compact set. II: Non-convex domains and higher dimensions ⋮ Sharp spectral bounds on starlike domains ⋮ On the behavior of the first eigenvalue of the \(p\)-Laplacian with Robin boundary conditions as \(p\) goes to 1 ⋮ On the second Robin eigenvalue of the Laplacian ⋮ Second domain variation for problems with Robin boundary conditions ⋮ Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle ⋮ Estimates for Robin \(p\)-Laplacian eigenvalues of convex sets with prescribed perimeter ⋮ Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign ⋮ Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators ⋮ Local spectral optimisation for Robin problems with negative boundary parameter on quadrilaterals ⋮ Principal eigenvalues for generalised indefinite Robin problems ⋮ On the \(p\)-Laplacian with Robin boundary conditions and boundary trace theorems ⋮ Effective operators for Robin eigenvalues in domains with corners ⋮ A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter ⋮ Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds ⋮ Optimisation of the lowest Robin eigenvalue in the exterior of a compact set ⋮ Mean curvature bounds and eigenvalues of Robin Laplacians ⋮ The Robin Laplacian—Spectral conjectures, rectangular theorems ⋮ Spectral optimization for singular Schrödinger operators ⋮ A sharp isoperimetric inequality for the second eigenvalue of the Robin plate ⋮ Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones ⋮ A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter ⋮ The first Robin eigenvalue with negative boundary parameter ⋮ An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain ⋮ On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue ⋮ The Bilaplacian with Robin Boundary Conditions

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