We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on domains of Rd of finite measure. The proof relies on asymptotically sharp lower and upper bounds that we develop for the Riesz mean R2(z). Lower bounds are obtained by making use of the so-called "averaged variational principle."Upper bounds are obtained in the spirit of Berezin-Li-Yau. Moreover, we state a conjecture for the second term in Weyl's law and prove its correctness in two special cases: balls in Rd and bounded intervals in R.
On the spectral asymptotics for the buckling problem / Buoso, D.; Luzzini, P.; Provenzano, L.; Stubbe, J.. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 62:12(2021), p. 121501. [10.1063/5.0069529]
On the spectral asymptotics for the buckling problem
Provenzano L.
;
2021
Abstract
We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on domains of Rd of finite measure. The proof relies on asymptotically sharp lower and upper bounds that we develop for the Riesz mean R2(z). Lower bounds are obtained by making use of the so-called "averaged variational principle."Upper bounds are obtained in the spirit of Berezin-Li-Yau. Moreover, we state a conjecture for the second term in Weyl's law and prove its correctness in two special cases: balls in Rd and bounded intervals in R.| File | Dimensione | Formato | |
|---|---|---|---|
|
Buoso_spectralAsymptotics_2021.pdf
solo gestori archivio
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
368.97 kB
Formato
Adobe PDF
|
368.97 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
