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Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains

Frank, R. L. and Laptev, A. (2019) Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains. St. Petersburg Mathematical Journal, 30 (3). pp. 573-589. ISSN 1061-0022. https://resolver.caltech.edu/CaltechAUTHORS:20180604-111721567

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Abstract

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schrödinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here it is shown that in the case of Dirichlet boundary conditions the constant in this bound can be chosen independently of the domain.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/spmj/1559DOIArticle
https://arxiv.org/abs/1712.03167arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, R. L.0000-0001-7973-4688
Additional Information:© 2019 American Mathematical Society. Received 8 Dec. 2017. Article electronically published on April 12, 2019. Partially supported by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) and by a grant of the Russian Federation Government under the supervision of a leading scientist at the Siberian Federal University, grant no. 14.Y26.31.0006 (A.L.). The authors are grateful to Timo Weidl for extensive discussions related to this material and to Grigori Rozenblum for many helpful remarks on the manuscript.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Russian FederationUNSPECIFIED
Siberian Federal University14.Y26.31.0006
Subject Keywords:Schrödinger operator, Dirichlet Laplacian, Neumann Laplacian, Trudinger inequality
Issue or Number:3
Record Number:CaltechAUTHORS:20180604-111721567
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180604-111721567
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86786
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Jun 2018 18:24
Last Modified:03 Oct 2019 19:48

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