  In this work, we study the solvability of a boundary value problem for the
magneto-hydrostatic equations originally proposed by Grad and Rubin in the late
50's. The proof relies on a fixed point argument which combines the so-called
current transport method together with H\"older estimates for a class of
non-convolution singular integral operators. The same method allows to solve an
analogous boundary value problem for the steady incompressible Euler equations.
