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Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 250–272 (Mi aa1603)  

Research Papers

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

R. L. Frankab, A. Laptevcd

a Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333, München, Germany
b Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
c Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
d Institut Mittag-Leffler, Auravägen 17, 182 60, Djursholm, Sweden

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.

Keywords: Schrödinger operator, Dirichlet Laplacian, Neumann Laplacian, Trudinger inequality.

Funding Agency Grant Number
National Science Foundation DMS-1363432
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
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 № 14.Y26.31.0006 (A.L.).


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Document Type: Article
Received: 08.12.2017
Language: English

Citation: R. L. Frank, A. Laptev, “Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains”, Algebra i Analiz, 30:3 (2018), 250–272

Citation in format AMSBIB
\Bibitem{FraLap18}
\by R.~L.~Frank, A.~Laptev
\paper Bound on the number of negative eigenvalues of two-dimensional Schr\"odinger operators on domains
\jour Algebra i Analiz
\yr 2018
\vol 30
\issue 3
\pages 250--272
\mathnet{http://mi.mathnet.ru/aa1603}
\elib{http://elibrary.ru/item.asp?id=32855073}


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