Quasilinear elliptic system arising in a three-dimensional type-II superconductor for infinite κ Original Research Article

We study a quasilinear elliptic system arising in a three-dimensional superconductor Ω. This model is formally derived from the Ginzburg–Landau energy at κ=+∞ for a Meissner solution. If the tangential trace of the magnetic field View the MathML source is given on ∂Ω, we prove the existence of a unique solution for small data, and nonexistence for large data. On the other hand we prove that the current View the MathML source is such that View the MathML source is maximum on the boundary ∂Ω.