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 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.
Complementary asymptotically sharp estimates for eigenvalue means of laplacians / Harrell, Evans; Provenzano, Luigi; Stubbe, Joachim. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 11:(2021), pp. 8405-8450. [10.1093/imrn/rnz085]
Complementary asymptotically sharp estimates for eigenvalue means of laplacians
Luigi Provenzano
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2021
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 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.| File | Dimensione | Formato | |
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