Isoperimetric monotonicity and isoperimetric inequalities of Payne-Rayner type for the first eigenfunction of the Helmholtz problem

DOI10.1007/BF00946975zbMath0472.35032MaRDI QIDQ1157715

Marie-Therese Kohler-Jobin

Publication date: 1981

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

boundary value problemfirst eigenfunctioninequality of Payne-Raynerisoperimetric properties

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (9)

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on 𝑅𝐶𝐷(𝐾,𝑁) spaces ⋮ An estimate for the \(L^p\)-norms of a stress function for finitely connected plane domains ⋮ Isoperimetric monotony of the \(L^p\)-norm of the warping function of a plane simply connected domain ⋮ Two isoperimetric inequalities for the Sobolev constant ⋮ Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature ⋮ Isoperimetric inequalities for a wedge-like membrane ⋮ Randwertprobleme und Methode der inneren Parallelen: eine gemeinsame Erweiterung zweier Ungleichungen von Pólya ⋮ Isoperimetric bounds for the first eigenvalue of the Laplacian ⋮ A reverse Hölder inequality for extremal Sobolev functions

Cites Work

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• Bounds for the solutions of boundary value problems
• Sur la premiere fonction propre d'une membrane: une extension à N dimensions de l'inégalité isoperimetrique de Payne-Rayner
• Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie
• An isoperimetric inequality for the first eigenfunction in the fixed membrane problem
• Some isoperimetric norm bounds for solutions of the Helmholtz equation
• On the mean value of the fundamental mode in the fixed membrane problem
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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