  We study the possibility of constructing steady magnetic fields satisfying
the force balance equation of ideal magnetohydrodynamics with tangential
boundary conditions in asymmetric confinement vessels, i.e. bounded regions
that are not invariant under continuous Euclidean isometries (translations,
rotations, or their combination). This problem is often encountered in the
design of next-generation fusion reactors. We show that such configurations are
possible if one relaxes the standard assumption that the vessel boundary
corresponds to a pressure isosurface. We exhibit a smooth solution that
possesses an Euclidean symmetry and yet solves the boundary value problem in an
asymmetric ellipsoidal domain while sustaining a non-vanishing pressure
gradient. This result provides a definitive answer to the problem of existence
of regular ideal magnetofluidostatic equilibria in asymmetric bounded domains.
The question remains open whether regular asymmetric solutions of the boundary
value problem exist.
