We obtain estimates for sums of eigenvalues of the free plate under tension in terms of the dimension of the ambient space, the volume of the domain, and the tension parameter. We consequently obtain similar estimates for the eigenvalues. Our results generalize those of Kröger for the free membrane contained in [16].
Brandolini B., Chiacchio F., Langford J.J. (2020). Estimates for sums of eigenvalues of the free plate via the Fourier transform. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 19(1), 113-122 [10.3934/cpaa.2020007].
Estimates for sums of eigenvalues of the free plate via the Fourier transform
Brandolini B.
;
2020-01-01
Abstract
We obtain estimates for sums of eigenvalues of the free plate under tension in terms of the dimension of the ambient space, the volume of the domain, and the tension parameter. We consequently obtain similar estimates for the eigenvalues. Our results generalize those of Kröger for the free membrane contained in [16].
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