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Eigenvalue estimates for magnetic Schrödinger operators in domains

Authors: Rupert L. Frank, Ari Laptev and Stanislav Molchanov
Journal: Proc. Amer. Math. Soc. 136 (2008), 4245-4255
MSC (2000): Primary 35P15; Secondary 35J10
Published electronically: July 29, 2008
MathSciNet review: 2431037
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Abstract: Inequalities are derived for sums and quotients of eigenvalues of magnetic Schrödinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.

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Additional Information

Rupert L. Frank
Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
Address at time of publication: Department of Mathematics, Princeton University, Fine Hall, Princeton, New Jersey 08544

Ari Laptev
Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom – and – Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden

Stanislav Molchanov
Affiliation: Department of Mathematics, University of North Carolina, Charlotte, North Caro- lina 28223-0001

Keywords: Eigenvalue bounds, semi-classical estimates, Laplace operator, magnetic Schr\"odinger operator
Received by editor(s): May 29, 2007
Published electronically: July 29, 2008
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2008 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.

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