Gauge Invariant Eigenvalue Problems in $\mathbb {R}^n$ and in $\mathbb {R}^n_+$
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- by Kening Lu and Xing-Bin Pan
- Trans. Amer. Math. Soc. 352 (2000), 1247-1276
- DOI: https://doi.org/10.1090/S0002-9947-99-02516-7
- Published electronically: October 6, 1999
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Abstract:
This paper is devoted to the study of the eigenvalue problems for the Ginzburg-Landau operator in the entire plane ${\mathbb {R}}^{2}$ and in the half plane ${\mathbb {R}}^{2}_{+}$. The estimates for the eigenvalues are obtained and the existence of the associate eigenfunctions is proved when $curl A$ is a non-zero constant. These results are very useful for estimating the first eigenvalue of the Ginzburg-Landau operator with a gauge-invariant boundary condition in a bounded domain, which is closely related to estimates of the upper critical field in the theory of superconductivity.References
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Bibliographic Information
- Kening Lu
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- MR Author ID: 232817
- Email: klu@math.byu.edu
- Xing-Bin Pan
- Affiliation: Center for Mathematical Sciences, Zhejiang University, Hangzhou 310027, P.R. China; Department of Mathematics, National University of Singapore, Singapore
- Email: matpanxb@nus.edu.sg
- Received by editor(s): November 1, 1996
- Received by editor(s) in revised form: December 18, 1997
- Published electronically: October 6, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1247-1276
- MSC (1991): Primary 82D55
- DOI: https://doi.org/10.1090/S0002-9947-99-02516-7
- MathSciNet review: 1675206