Isoperimetric Monotonicity: Some Properties and Conjectures (Connections between Isoperimetric Inequalities)

DOI10.1137/1030132zbMath0669.35089OpenAlexW1991542484WikidataQ122871579 ScholiaQ122871579MaRDI QIDQ3822610

Joseph Hersch

Publication date: 1988

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1030132

zbMATH Keywords

isoperimetric inequalitiestorsional rigidityestimation of eigenvaluesisoperimetric monotonicityPoisson and Helmholtz equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

An estimate for the \(L^p\)-norms of a stress function for finitely connected plane domains ⋮ Integral properties of the classical warping function of a simply connected domain ⋮ Isoperimetric monotony of the \(L^p\)-norm of the warping function of a plane simply connected domain ⋮ A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains ⋮ Two-sided estimate for the torsional rigidity of convex domain generalizing the Polya-Szegö and Makai inequalities ⋮ Isoperimetric inequalities for \(L^p\)-norms of the stress function of a multiply connected plane domain ⋮ Isoperimetric properties of Euclidean boundary moments of a simply connected domain ⋮ Numerical implementation of coherence for the example of the ``Swiss Cross ⋮ Payne type inequalities for \(L^p\)-norms of the warping functions ⋮ One-parameter monotone functionals connected with Stieltjes integrals

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