A quantitative Weinstock inequality for convex sets

DOI10.1007/s00526-019-1642-9zbMath1427.35165arXiv1903.04964OpenAlexW2990973433WikidataQ126767806 ScholiaQ126767806MaRDI QIDQ2007991

Gloria Paoli, Leonardo Trani, Domenico Angelo La Manna, Nunzia Gavitone

Publication date: 22 November 2019

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04964

zbMATH Keywords

Laplace operatorSteklov eigenvalue problemweighted isoperimetric inequalityfirst Steklov eigenvalueWeinstock inequality

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Estimates of eigenvalues in context of PDEs (35P15)

Related Items (10)

Sharp and quantitative estimates for the \(p\)-torsion of convex sets ⋮ An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole ⋮ Estimates for Robin \(p\)-Laplacian eigenvalues of convex sets with prescribed perimeter ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Some weighted isoperimetric inequalities in quantitative form ⋮ The orthotropic \(p\)-Laplace eigenvalue problem of Steklov type as \(p\rightarrow+\infty\) ⋮ Stability and instability issues of the Weinstock inequality ⋮ A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian ⋮ A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter ⋮ 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 quantitative Faber-Krahn inequality for the Robin Laplacian
• The quantitative isoperimetric inequality and related topics
• A weighted isoperimetric inequality and applications to symmetrization
• Sets of Finite Perimeter and Geometric Variational Problems
• Stability in the Isoperimetric Problem for Convex or Nearly Spherical Domains in R n
• 7 Spectral inequalities in quantitative form
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