Published May 16, 2017
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Pόlya's conjecture in the presence of a constant magnetic field
- Creators
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Frank, Rupert L.
- Loss, Michael
- Weidl, Timo
Abstract
We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Pόlya's conjecture is not true in the presence of a magnetic field.
Additional Information
© 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. (Submitted on 4 Oct 2007) This work had its gestation at the workshop 'Low eigenvalues of Laplace and Schrödinger operators' which was held at AIM in May 2006. The support of AIM is gratefully acknowledged. This work has been partially supported by DAAD grant D/06/49117 (R. F.), NSF grant DMS 0600037 (M. L.) and DFG grant WE-1964/2-1 (T.W.), as well as by the DAAD-STINT PPP program (R. F. and T. W.).Attached Files
Submitted - 0710.1078.pdf
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Additional details
- Eprint ID
- 77326
- Resolver ID
- CaltechAUTHORS:20170510-073002205
- D/06/49117
- Deutscher Akademischer Austauschdienst (DAAD)
- DMS 0600037
- NSF
- WE-1964/2-1
- Deutsche Forschungsgemeinschaft (DFG)
- Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
- Created
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2017-05-16Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field