Geodesic
Line-energy Ginzburg-Landau models : zero-energy states
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 187-202

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We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful analysis of the corresponding weak solutions by the method of characteristics.

Classification : 35B65, 35J60, 35L65, 74G65, 82D30 
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     author = {Jabin, Pierre-Emmanuel and Otto, Felix and Perthame, Beno\^It},
     title = {Line-energy {Ginzburg-Landau} models : zero-energy states},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {187--202},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     year = {2002},
     mrnumber = {1994807},
     zbl = {1072.35051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_187_0/}
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Jabin, Pierre-Emmanuel; Otto, Felix; Perthame, BenoÎt. Line-energy Ginzburg-Landau models : zero-energy states. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 187-202. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_187_0/