  We generalize the classic calculations by Rytova and Keldysh of screened
Coulomb interaction in semiconductor thin films to systems with anisotropic
permittivity tensor. Explicit asymptotic expressions for electrostatic
potential energy of interaction in the weakly anisotropic case are found in
closed analytical form. The case of strong in-plane anisotropy, however,
requires evaluation of the inverse Fourier transform of $1/(k+Ak_x^2+Bk_y^2)$,
which, at present, remains unresolved.
