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research article
Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians
June 1, 2021
We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend to infinity. We accomplish this in the framework of the Riesz mean R-1(z) of the eigenvalues by applying the averaged variational principle with families of test functions that have been corrected for boundary behaviour.
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Type
research article
Web of Science ID
WOS:000731069300010
Authors
Publication date
2021-06-01
Publisher
Published in
Volume
2021
Issue
11
Start page
8405
End page
8450
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
January 1, 2022