We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new _L_∞ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].
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Bernard Helffer, Søren Fournais, Bulk superconductivity in Type II superconductors near the second critical ﬁeld. J. Eur. Math. Soc. 12 (2010), no. 2, pp. 461–470