Publication

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Joachim Stubbe, Luigi Provenzano
2021
Journal Articles

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/89fcf677-6ba3-4f7b-9c9d-180673fa3d06

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Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

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