Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

Evans M. Harrell II; Luigi Provenzano; Joachim Stubbe

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arXiv · 1806.10366

Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

Evans M. Harrell II·Luigi Provenzano·Joachim Stubbe

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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 $R_1(z)$ 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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BibTeX RIS

Evans M. Harrell II, Luigi Provenzano, Joachim Stubbe. 2018-06-27. Complementary asymptotically sharp estimates for eigenvalue means of Laplacians. https://arxiv.org/abs/1806.10366

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