Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

2018/06/27 by Harrell, Evans M., Provenzano, Luigi, Stubbe, Joachim
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1806.10366

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 Kröger inequalities in the limit as the eigenvalues tend to infinity. We accomplish this in the framework of the Riesz mean R₁(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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