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Comptes Rendus Mathématique
Volume 343, n° 1
pages 63-68 (juillet 2006)
Doi : 10.1016/j.crma.2006.05.013
Received : 23 January 2006 ;  accepted : 15 May 2006
Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain
Nonexistence des minimizers de Ginzburg-Landau avec le degré prescrit sur la frontière dʼun domaine doublement connexe
 

Leonid Berlyand a, 1 , Dmitry Golovaty b, 2 , Volodymyr Rybalko c, 3
a Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA 
b Department of Theoretical and Applied Mathematics, The University of Akron, Akron, OH 44325, USA 
c Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61164 Kharkov, Ukraine 

Abstract

Let , be bounded simply connected domains in  , and let  . In the annular domain   we consider the class   of complex valued maps having modulus 1 and degree 1 on and .

We prove that, when  , there exists a finite threshold value   of the Ginzburg-Landau parameter such that the minimum of the Ginzburg-Landau energy   not attained in   when   while it is attained when  . To cite this article: L. Berlyand et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Soient , des ouverts bornés, simplement connexes de  , et soit  . Dans le domaine annulaire   on considère une classe   des applications à valeurs complexes ayant le module égal à 1 et le degré 1 sur et .

On montre que, si  , alors il existe une valeur critique finie   du paramètre de Ginzburg-Landau, telle que le minimum de lʼénergie de Ginzburg-Landau   nʼest pas atteint dans   pour  , tandis quʼil est attaint pour  . Pour citer cet article : L. Berlyand et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
1  Supported by the NSF grant DMS-0204637.
2  Supported by the NSF grant DMS-0407361.
3  Supported by the grant GP/F8/0045 8/308-2004.


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