Geodesic
Distribution of vortices in a type-II superconductor as a free boundary problem: existence and regularity via Nash-Moser theory
Alexis Bonnet1 ; Régis Monneau2
1Université de Cergy-Pontoise, France
2CERMICS - ENPC, Marne-La-Vallée, France
Interfaces and free boundaries, Tome 2 (2000) no. 2, pp. 181-200

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DOI

This paper is concerned with a model describing the distribution of vortices in a Type-II superconductor. These vortices are distributed continuously and occupy an unknown region D with [part]D representing the free boundary. The problem is set as follows: two constants H0 > H1 > 0 are given, to find an open subset D of the smooth bounded open set [ohm] [sub] R2 and a function H defined on [ohm]\D such that {div(F(|[nabla] H|2) [nabla] H) - H=0 in [ohm]\D where the function F is analytic positive increasing H=H0 on [par][ohm] H=H1 on [par]D [par]H[horbar][par]n = [par]D. Here we prove the existence of a solution with a domain D having an analytic boundary. We use the Nash-Moser inverse function theorem applied to a degenerate case.
DOI : 10.4171/ifb/17
Classification : 46-XX, 60-XX
Mots-clés : superconductor; free boundary problems

Alexis Bonnet  1   ; Régis Monneau  2

1 Université de Cergy-Pontoise, France
2 CERMICS - ENPC, Marne-La-Vallée, France 
Alexis Bonnet; Régis Monneau. Distribution of vortices in a type-II superconductor as a free boundary problem: existence and regularity via Nash-Moser theory. Interfaces and free boundaries, Tome 2 (2000) no. 2, pp. 181-200. doi: 10.4171/ifb/17
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     author = {Alexis Bonnet and R\'egis Monneau},
     title = {Distribution of vortices in a {type-II} superconductor as a free boundary problem: existence and regularity via {Nash-Moser} theory},
     journal = {Interfaces and free boundaries},
     pages = {181--200},
     year = {2000},
     volume = {2},
     number = {2},
     doi = {10.4171/ifb/17},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/17/}
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