Volume 43_4_(2022)_267-314

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