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We consider superconductors of Type II near the transition from the 'bulksuperconducting' to the 'surface superconducting' state. We prove a new$L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from theboundary. This solves an open problem posed by Aftalion and Serfaty.

Bulk superconductivity in Type II superconductors near the second critical ﬁeld