Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains

Authors:
Xing-Bin Pan and Keng-Huat Kwek

Journal:
Trans. Amer. Math. Soc. **354** (2002), 4201-4227

MSC (2000):
Primary 35Q55, 81Q10, 82D55

Published electronically:
May 15, 2002

MathSciNet review:
1926871

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We establish an asymptotic estimate of the lowest eigenvalue of the Schrödinger operator with a magnetic field in a bounded -dimensional domain, where curl vanishes non-degenerately, and 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.

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Additional 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

DOI:
https://doi.org/10.1090/S0002-9947-02-03033-7

Keywords:
Schr\"{o}dinger operator with a magnetic field,
eigenvalue,
Ginzburg-Landau system,
superconductivity,
nucleation,
upper critical field,
Sturm-Liouville operator,
Riccati type equation

Received by editor(s):
July 17, 2000

Received by editor(s) in revised form:
March 13, 2001

Published electronically:
May 15, 2002

Article copyright:
© Copyright 2002
American Mathematical Society