A free boundary problem in magnetostatics
A. Bossavit · 2020
Magnetostatics consists in finding vector fields b and h suchthat div b = 0, rot h = j (j is given), and b = Γ(h), where Γ is the subgradient of a convex functional U (the magnetic coenergy). When U is the sum of a quadratic functional and of a support functional, a 2-phase Stefan problem results, a “vector” Stefan problem so to speak, because the unknown is a vector-field, not a function, like for instance the temperature.