Shape optimization for the Steklov problem in higher dimensions

DOI10.1016/j.aim.2019.03.011zbMath1419.35139arXiv1711.04381OpenAlexW2962973976MaRDI QIDQ2631936

Ailana M. Fraser, Richard M. Schoen

Publication date: 16 May 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.04381

zbMATH Keywords

optimizationSteklov eigenvalue

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) PDEs on manifolds (35R01)

Related Items (20)

Tubular excision and Steklov eigenvalues ⋮ Generic properties of Steklov eigenfunctions ⋮ Discs area-minimizing in mean convex Riemanniann-manifolds ⋮ A shape optimization problem for the first mixed Steklov-Dirichlet eigenvalue ⋮ Higher dimensional surgery and Steklov eigenvalues ⋮ Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary ⋮ An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole ⋮ The upper bound of the harmonic mean of the Steklov eigenvalues in curved spaces ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Some results on higher eigenvalue optimization ⋮ Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index ⋮ Sharp Steklov upper bound for submanifolds of revolution ⋮ A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter ⋮ Weinstock inequality in higher dimensions ⋮ Stability and instability issues of the Weinstock inequality ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ The overdetermined problem and lower bound estimate on the first nonzero Steklov eigenvalue of \(p\)-Laplacian ⋮ Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue ⋮ Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue ⋮ Laplace and Steklov extremal metrics via \(n\)-harmonic maps

Cites Work

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• Sharp eigenvalue bounds and minimal surfaces in the ball
• Isoperimetric control of the Steklov spectrum
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem
• Upper bounds for Steklov eigenvalues on surfaces
• Some inequalities for Stekloff eigenvalues
• Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
• Weinstock inequality in higher dimensions
• Heat invariants of the Steklov problem
• Spectral geometry of the Steklov problem (survey article)
• On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
• Variational aspects of Laplace eigenvalues on Riemannian surfaces
• Sums of reciprocal Stekloff eigenvalues

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