On approximation of Ginzburg-Landau minimizers by S1-valued maps in domains with vanishingly small holes

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Berlyand, Leonid¹  Golovaty, Dmitry²  Iaroshenko, Oleksandr¹  Rybalko, Volodymyr³ 

[1] Penn State Univ, Dept Math, 337 McAllister Bldg, University Pk, PA 16802 USA

[2] Univ Akron, Dept Math, Akron, OH 44325 USA

[3] BI Verkin Inst Low Temp Phys & Engn, Math Div, Kharkov, Ukraine

关键词: Ginzburg-Landau;    Superconductivity;    Vortex;    Boundary value problem;    Multiply-connected domain;   

DOI  :  10.1016/j.jde.2017.09.037

来源: Elsevier

【 摘 要 】

We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau parameter vs. hole radius) is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg-Landau problems in the classes of S-1-valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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