Extremum problems of Laplacian eigenvalues and generalized Polya conjecture

DOI10.1007/s11401-017-1080-yOpenAlexW2593605192WikidataQ123230048 ScholiaQ123230048MaRDI QIDQ2358534

Fang-Hua Lin

Publication date: 15 June 2017

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-017-1080-y

zbMATH Keywords

regularity of minimizersLaplacian eigenvaluesWeyl asymptoticsextremum problemsPolya's conjecturespliting equality

Mathematics Subject Classification ID

Partial differential equations (35-XX) Calculus of variations and optimal control; optimization (49-XX) Manifolds and cell complexes (57-XX)

Related Items (4)

Pólya's conjecture for Euclidean balls ⋮ Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem ⋮ Large \(m\) asymptotics for minimal partitions of the Dirichlet eigenvalue ⋮ On a Rayleigh-Faber-Krahn Inequality for the Regional Fractional Laplacian

Cites Work

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• Existence of minimizers for spectral problems
• On spectral minimal partitions: a survey
• On the Schrödinger equation and the eigenvalue problem
• An existence result for a class of shape optimization problems
• Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
• The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H. C. Yang
• Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian
• On optimal shape design
• Lipschitz regularity of the eigenfunctions on optimal domains
• Weyl asymptotic formula for the Laplacian on domains with rough boundaries
• Variational methods in shape optimization problems
• One-dimensional cohomologies of discrete subgroups
• An optimal partition problem for eigenvalues
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• On the Eigenvalues of Vibrating Membranes^†
• Minimization of the third eigenvalue of the Dirichlet Laplacian
• Range of the first two eigenvalues of the laplacian
• Can One Hear the Shape of a Drum?
• COVARIANT AND CONTRAVARIANT SYMBOLS OF OPERATORS
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• Lectures on spectral theory of elliptic operators

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