  We consider time-harmonic acoustic scattering by planar sound-soft
(Dirichlet) and sound-hard (Neumann) screens. In contrast to previous studies,
in which the domain occupied by the screen is assumed to be Lipschitz or
smoother, we consider screens occupying an arbitrary bounded open set in the
plane. Thus our study includes cases where the closure of the domain occupied
by the screen has larger planar Lebesgue measure than the screen, as can
happen, for example, when the screen has a fractal boundary. We show how to
formulate well-posed boundary value problems for such scattering problems, our
arguments depending on results on the coercivity of the acoustic single-layer
and hypersingular boundary integral operators, and on properties of Sobolev
spaces on general open sets which appear to be new. Our analysis teases out the
explicit wavenumber dependence of the continuity and coercivity constants of
the boundary integral operators, viewed as mappings between fractional Sobolev
spaces, this in part extending previous results of Ha-Duong. We also consider
the complementary problem of propagation through a bounded aperture in an
infinite planar screen.
