Nucleation of instability of the Meissner state of 3-dimensional superconductors (Q2466831)

This paper deals with the qualitative analysis of a nonlinear partial differential system involving the differential operator curl\(^2\) in a 3--dimensional domain. After obtaining \(H^2\) estimates of weak solutions, the authors classify the solutions of limiting equations in \(\mathbb R^3\) and in \(\mathbb R^3_+\). Next, by combining \(C^{2,\alpha}\) estimates and a blow-up argument, they derive a criterion for the boundary data that implies solvability. The asymptotic behavior of solutions as the parameter \(\lambda\) approaches 0 is also deduced in the present paper.