Stability and instability issues of the Weinstock inequality

DOI10.1090/tran/8302zbMath1458.35287arXiv2004.07784OpenAlexW3094442720MaRDI QIDQ4963642

Mickaël Nahon, Dorin Bucur

Publication date: 19 February 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07784

zbMATH Keywords

Steklov eigenvalue problem on planar domains

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15)

Related Items (9)

Spectral stability of the Steklov problem ⋮ A comparison between Neumann and Steklov eigenvalues ⋮ An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces ⋮ Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems ⋮ Asymptotic behaviour of the Steklov spectrum on dumbbell domains ⋮ Symmetry results for variational energies on convex polygons ⋮ Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

Cites Work

• Spectral optimization for the Stekloff-Laplacian: The stability issue
• The Steklov spectrum on moving domains
• The quantitative Faber-Krahn inequality for the Robin Laplacian
• Upper bounds for Steklov eigenvalues on surfaces
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Shape variation and optimization. A geometrical analysis
• \(L^\infty\) bounds of Steklov eigenfunctions and spectrum stability under domain variation
• A quantitative Weinstock inequality for convex sets
• Spectral geometry of the Steklov problem (survey article)
• The sharp quantitative isoperimetric inequality
• Shape optimization for the Steklov problem in higher dimensions
• 5 Spectral geometry of the Steklov problem
• An Extension of Schwarz's Lemma
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