  Answering a question left open in \cite{MZ2}, we show for general symmetric
hyperbolic boundary problems with constant coefficients, including in
particular systems with characteristics of variable multiplicity, that the
uniform Lopatinski condition implies strong $L^2$ well-posedness, with no
further structural assumptions. The result applies, more generally, to any
system that is strongly $L^2$ well-posed for at least one boundary condition.
The proof is completely elementary, avoiding reference to Kreiss symmetrizers
or other specific techniques. On the other hand, it is specific to the
constant-coefficient case; at least, it does not translate in an obvious way to
the variable-coefficient case. The result in the hyperbolic case is derived
from a more general principle that can be applied, for example, to parabolic or
partially parabolic problems like the Navier-Stokes or viscous MHD equations
linearized about a constant state or even a viscous shock.
