Solvability of MHS equations with Grad-Rubin boundary conditions in general domains

In this paper we study the solvability of the magnetohydrostatic equations with Grad-Rubin boundary conditions in general domains. Earlier results for this problem were obtained in the recent years by D. Alonso-Orán and J. L. L. Velázquez, where particularly simple geometries were considered. In this article we develop a theory that allows to solve these boundary value problems for a larger class of domains. We will give precise applications to more physically relevant situations, like the case of the space between two circumferences or spheres and domains close to them.