  For a compact spinc manifold $X$ with boundary $b_1(\partial X)=0$, we
consider moduli spaces of solutions to the Seiberg-Witten equations in a
generalized double Coulomb slice in $L^2_1$ (i.e., $W^{1,2}$) Sobolev
regularity. We prove they are Hilbert manifolds, prove denseness and
"semi-infinite-dimensionality" properties of the restriction to $\partial X$,
and establish a gluing theorem.
  To achieve these, we prove a general regularity theorem and a strong unique
continuation principle for Dirac operators, and smoothness of a restriction map
to configurations of higher regularity on the interior, all of which are of
independent interest.
