Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (2): 299-306.

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New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations

Huang Decheng1, Chen Shouxin2   

  1. 1 School of Mathematics and Computers, Xinyang Vocational and Technical College, Henan Xinyang 464000;
    2 Institute of Contemporary Mathmatics, School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004
  • Received:2016-06-13 Revised:2016-10-22 Online:2017-04-26 Published:2017-04-26
  • Supported by:
    Supported by the NSFC (11471100, 11471099) and the Foundation and Frontier Project of Department of Science and Technology of Henan Province (142300410110)

Abstract: In this paper we use a direct variational method, with the help of Hardy type inequality, to give a new proof for the existence of minimizing energy solutions for the Ginzburg-Landau equations in R2 coupled with an external magnetic field or a source current. Moreover, the solution satisfies the Coulomb gauge.

Key words: Ginzburg-Landau equations, Variational method, Hardy type inequality, Existence of solutions

CLC Number: 

  • O175.25
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