Some inequalities for Stekloff eigenvalues

DOI10.1007/BF00248412zbMath0315.35069MaRDI QIDQ1221055

M. M. Schiffer, Joseph Hersch, Lawrence E. Payne

Publication date: 1974

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Mathematics Subject Classification ID

Related Items (40)

Numerical calculation of extremal Steklov eigenvalues in 3D and 4D ⋮ Upper bounds for the Steklov eigenvalues on trees ⋮ Trace and inverse trace of Steklov eigenvalues ⋮ The method of fundamental solutions applied to boundary eigenvalue problems ⋮ Shape optimization for the Steklov problem in higher dimensions ⋮ Exact constants in Poincaré type inequalities for functions with zero mean boundary traces ⋮ Dirichlet-to-Neumann maps for differential forms on graphs and their eigenvalues ⋮ Isoperimetric bounds for lower-order eigenvalues ⋮ A higher dimensional generalization of Hersch-Payne-Schiffer inequality for Steklov eigenvalues ⋮ Existence and classification of \(\mathbb{S}^1\)-invariant free boundary minimal annuli and Möbius bands in \(\mathbb{B}^n\) ⋮ Higher dimensional surgery and Steklov eigenvalues ⋮ Spatial decay in transient heat conduction for general elongated regions ⋮ Computational Methods for Extremal Steklov Problems ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Spectral optimization for the Stekloff-Laplacian: The stability issue ⋮ The first Steklov eigenvalue, conformal geometry, and minimal surfaces ⋮ Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces ⋮ On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues ⋮ Estimates for higher Steklov eigenvalues ⋮ Some results on higher eigenvalue optimization ⋮ Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems ⋮ Harmonic functions satisfying a radiation boundary condition ⋮ The Steklov Problem on Differential Forms ⋮ Weyl-type bounds for Steklov eigenvalues ⋮ Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems ⋮ Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures ⋮ A Reilly inequality for the first non-zero eigenvalue of a class of operators on Riemannian manifold ⋮ Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds ⋮ Optimal Shapes Maximizing the Steklov Eigenvalues ⋮ Isoperimetric control of the Steklov spectrum ⋮ A Reilly inequality for the first Steklov eigenvalue ⋮ Trace and inverse trace of Steklov eigenvalues. II. ⋮ Steklov eigenvalues and quasiconformal maps of simply connected planar domains ⋮ Sharp bounds for the first non-zero Stekloff eigenvalues ⋮ Weinstock inequality in higher dimensions ⋮ Nodal sets of Steklov eigenfunctions ⋮ Maximal convex combinations of sequential Steklov eigenvalues ⋮ Steklov eigenvalues of reflection-symmetric nearly circular planar domains ⋮ An isoperimetric inequality and the first Steklov eigenvalue ⋮ Robin spectrum: two disks maximize the third eigenvalue

Cites Work

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• Über das Stekloffsche Eigenwertproblem: Isoperimetrische Ungleichungen für symmetrische Gebiete
• Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff's type
• Inequalities for membrane and Stekloff eigenvalues
• On symmetric membranes and conformal radius: Some complements to Polya's and Szegö's inequalities
• Various types of orthogonalization
• Convexity of functionals by transplantation
• On the characteristic frequencies of a symmetric membrane
• New isoperimetric inequalities for eigenvalues and other physical quantities
• An isoperimetric sloshing problem
• Some Isoperimetric Inequalities for Harmonic Functions
• Asymptotic Behavior of Stekloff Eigenvalues and Eigenfunctions

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