  We study the electrostatic responses (i.e. retardation effects due to the
propagation of electromagnetic waves are ignored) of a linear homogeneous and
anisotropic (LHA) dielectric film to an arbitrary external electrostatic
potential, which may be generated by charges located either inside or outside
it. A formalism is developed to calculate the polarization charges induced in
the film. In our derivation, the idea is exploited that a physical boundary can
be looked upon as a region of rapid variation in polarization rather than a
simple geometric separation. With this no boundary conditions are needed in
solving the relevant electrostatics problem. Our approach makes it clear that
the responses consist of two contributions, one arising from the very presence
of surfaces while the other existing even in an infinite medium. The approach
can be applied not just to electrostatic but also many problems and is of great
pedagogical value. In light of the results, we discuss graphene plasma waves
under the influence of a LHA dielectric film such as a few-layer hexagonal
boron nitride. It is found that the dispersion of these waves is strongly
affected by the anisotropy at wavelengths comparable to the film thickness.
