Semiclassical bounds for spectra of biharmonic operators

Abstract

We provide complementary semiclassical bounds for the Riesz means $R_1(z)$ of the eigenvalues of various biharmonic operators, with a second term in the expected power of $z$. The method we discuss makes use of the averaged variational principle (AVP), and yields two-sided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.

References in corpus (2)

• Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain
• On the remainder term of the Berezin inequality on a convex domain

Cited by in corpus (1)

• On the spectral asymptotics for the buckling problem