The fixed boundary equilibrium problem (also called the “inverse equilibrium problem” by some authors) refers to the case where the shape of a boundary magnetic surface is given and one is asked to solve the equilibrium within this magnetic surface. To make it convenient to deal with the shape of the boundary, one usually uses a general coordinates system which has one coordinate surface coinciding with the given magnetic surface. This makes it trivial to deal with the irregular boundary. To obtain the equilibrium, one needs to solve the GS equation in the general coordinate system.