On the spectral asymptotics for the buckling problem

Abstract. We provide a direct proof of Weyl’s law for the buckling eigenvalues of the biharmonic operator on a wide class of domains of R including bounded Lipschitz domains. 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 inWeyl’s law and prove its correctness in two special cases: balls in R and bounded intervals in R.

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