Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains
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- by Xing-Bin Pan and Keng-Huat Kwek
- Trans. Amer. Math. Soc. 354 (2002), 4201-4227
- DOI: https://doi.org/10.1090/S0002-9947-02-03033-7
- Published electronically: May 15, 2002
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Abstract:
We establish an asymptotic estimate of the lowest eigenvalue $\mu (b\mathbf {F})$ of the Schrödinger operator $-\nabla _{b\mathbf {F}}^{2}$ with a magnetic field in a bounded $2$-dimensional domain, where curl $\mathbf {F}$ vanishes non-degenerately, and $b$ is a large parameter. Our study is based on an analysis on an eigenvalue variation problem for the Sturm-Liouville problem. Using the estimate, we determine the value of the upper critical field for superconductors subject to non-homogeneous applied magnetic fields, and localize the nucleation of superconductivity.References
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Bibliographic Information
- Xing-Bin Pan
- Affiliation: Center for Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China; and Department of Mathematics, National University of Singapore, Singapore 119260
- Email: matpanxb@nus.edu.sg
- Keng-Huat Kwek
- Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260
- Address at time of publication: The Logistics Institute—Asia Pacific National University of Singapore, Singapore 119260
- Received by editor(s): July 17, 2000
- Received by editor(s) in revised form: March 13, 2001
- Published electronically: May 15, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 4201-4227
- MSC (2000): Primary 35Q55, 81Q10, 82D55
- DOI: https://doi.org/10.1090/S0002-9947-02-03033-7
- MathSciNet review: 1926871