Semiclassical bounds for spectra of biharmonic operators
Davide Buoso, Luigi Provenzano, Joachim Stubbe

Abstract. We provide complementary semiclassical bounds for the Riesz means R₁(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.

Rend. Mat. Appl. (7) 43 (2022) 267-314; pdf