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Isoperimetric inequalities of the fourth order Neumann eigenvalues. (English) Zbl 1503.35119

Summary: In this paper, we obtain some isoperimetric inequalities for the first \((n-1)\) eigenvalues of the fourth order Neumann Laplacian on bounded domains in an \(n\)-dimensional Euclidean space. Our result supports strongly the conjecture of L. M. Chasman [Commun. Math. Phys. 303, No. 2, 421–449 (2011; Zbl 1216.35152)].

MSC:

35P15 Estimates of eigenvalues in context of PDEs
53C40 Global submanifolds

Citations:

Zbl 1216.35152
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References:

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