Improved estimates for the Ginzburg-Landau equation : the elliptic case

Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 2, pp. 319-355.

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the $GL$-energy $E_{\epsilon }$ and the parameter $\epsilon$. These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

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