On the spectral asymptotics for the buckling problem

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.