Limiting jump conditions for Josephson junctions in Ginzburg-Landau theory

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We consider a superconducting/normal/superconducting Josephson junction modeled through the Ginzburg-Landau theory. When the normal material is sufficiently thin and the applied magnetic field is below the critical field of vortex nucleation, we prove to leading order that jump boundary conditions of the type predicted by de Gennes are satisfied across the junction.