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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. doi:10.1090/spmj/1559.

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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
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URLURL TypeDescription Paper
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.
Funding AgencyGrant Number
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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86786
Deposited By: Tony Diaz
Deposited On:04 Jun 2018 18:24
Last Modified:15 Nov 2021 20:42

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