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 Kroger for the free membrane contained in [P. Kroger, Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space, J. Funct. Anal., 106 (1992), 353–357].
Estimates for sums of eigenvalues of the free plate via the Fourier transform / Brandolini, Barbara; Chiacchio, Francesco; Langford, Jeffrey J.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:1(2020), pp. 113-122. [10.3934/cpaa.2020007]
Estimates for sums of eigenvalues of the free plate via the Fourier transform
BRANDOLINI, BARBARA;CHIACCHIO, FRANCESCO;
2020
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 Kroger for the free membrane contained in [P. Kroger, Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space, J. Funct. Anal., 106 (1992), 353–357].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
