Complementary asymptotically sharp estimates for eigenvalue means of Laplacians
Spectral Theory
2019-04-18 v2
Abstract
We present asymptotically sharp inequalities, containing a second term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kr\"oger inequalities in the limit as the eigenvalues tend to infinity. We accomplish this in the framework of the Riesz mean of the eigenvalues by applying the averaged variational principle with families of test functions that have been corrected for boundary behaviour.
Cite
@article{arxiv.1806.10366,
title = {Complementary asymptotically sharp estimates for eigenvalue means of Laplacians},
author = {Evans M. Harrell and Luigi Provenzano and Joachim Stubbe},
journal= {arXiv preprint arXiv:1806.10366},
year = {2019}
}