  An analytical validation is obtained for the evolution equation $$h_t=\Delta[
\mathcal{F}^{-1}(-aE \mathcal{F}(h)) - r/h^2 -\Delta h ],$$ introduced in
{\cite{TS}} by W.T. Tekalign and B.J. Spencer to describe the heteroepitaxial
growth of a two-dimensional thin film on an elastic substrate. In the
expression above, $h$ denotes the surface height of the film, $\mathcal{F}$ is
the Fourier transform, and $a$, $E$, $r$ are positive material constants.
Existence, uniqueness, and Lipschitz regularity in time for weak solutions are
proved, under suitable assumptions on the initial datum.
