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On the
Ashbaugh–Benguria conjecture about lower-order Dirichlet
eigenvalues of the Laplacian
Qiaoling Wang and Changyu Xia |
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Vol. 14 (2021), No. 7, 2069–2078
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Abstract |
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We prove an isoperimetric inequality for lower-order eigenvalues of the Dirichlet Laplacian on bounded domains of a Euclidean space which strengthens the celebrated Ashbaugh–Benguria inequality conjectured by Payne, Pólya and Weinberger on the ratio of the first two Dirichlet eigenvalues and makes an important step toward the proof of a conjecture by Ashbaugh and Benguria. |
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Keywords
Ashbaugh–Benguria conjecture, isoperimetric inequality,
eigenvalues, Dirichlet problem, Dirichlet eigenvalues,
Payne–Pólya–Weinberger conjecture
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Mathematical Subject Classification 2010
Primary: 35P15
Secondary: 58C40
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Milestones
Received: 7 December 2018
Accepted: 15 June 2020
Published: 10 November 2021
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Authors |
| Qiaoling Wang | |
| Departamento de Matemática Universidade de Brasília Brasília Brazil |
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| Changyu Xia | |
| Departamento de Matemática Universidade de Brasília Brasília Brazil |
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