Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems

DOI10.1007/s00039-021-00573-5zbMath1480.35305arXiv2004.10784OpenAlexW3195135477MaRDI QIDQ2232151

Mikhail Karpukhin, Alexandre Girouard, Jean Lagacé

Publication date: 4 October 2021

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.10784

zbMATH Keywords

Neumann eigenvaluessharp isoperimetric inequalities for Steklov eigenvalues

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) Elliptic equations on manifolds, general theory (58J05) PDEs on manifolds (35R01)

Related Items (12)

Tubular excision and Steklov eigenvalues ⋮ Dirichlet-to-Neumann maps for differential forms on graphs and their eigenvalues ⋮ Maximization of the second Laplacian eigenvalue on the sphere ⋮ A comparison between Neumann and Steklov eigenvalues ⋮ Weyl's law for the Steklov problem on surfaces with rough boundary ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces ⋮ Existence of harmonic maps and eigenvalue optimization in higher dimensions ⋮ Multiple tubular excisions and large Steklov eigenvalues ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue ⋮ Laplace and Steklov extremal metrics via \(n\)-harmonic maps

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