Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians-Reference-Cited by-同舟云学术

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Published:2019-05-03 Issue:11 Volume:2021 Page:8405-8450
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Harrell II Evans M¹,Provenzano Luigi²,Stubbe Joachim³

Affiliation:

1. School of Mathematics, Georgia Institute of Technology, Atlanta GA, USA

2. Università degli Studi di Padova, Dipartimento di Matematica, Via Trieste, Padova, Italy

3. EPFL, SB Institute of Mathematics, Station, CH Lausanne, Switzerland

Abstract

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 $R_1(z)$ of the eigenvalues by applying the averaged variational principle with families of test functions that have been corrected for boundary behaviour.

Funder

Swiss National Science Foundation

École Polytechnique Fédérale de Lausanne

Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni

Istituto Nazionale di Alta Matematica

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2021/11/8405/42309309/rnz085.pdf

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