  We study the initial-boundary value problem resulting from the linearization
of the plasma-vacuum interface problem in ideal compressible
magnetohydrodynamics (MHD). We suppose that the plasma and the vacuum regions
are unbounded domains and the plasma density does not go to zero continuously,
but jumps. For the basic state upon which we perform linearization we find two
cases of well-posedness of the "frozen" coefficient problem: the "gas
dynamical" case and the "purely MHD" case. In the "gas dynamical" case we
assume that the jump of the normal derivative of the total pressure is always
negative. In the "purely MHD" case this condition can be violated but the
plasma and the vacuum magnetic fields are assumed to be non-zero and
non-parallel to each other everywhere on the interface. For this case we prove
a basic a priori estimate in the anisotropic weighted Sobolev space $H^1_*$ for
the variable coefficient problem.
