Corner diffusion is shown to play a crucial role in determining the asympto
tic mound coarsening exponent in in the case of unstable epitaxial growth o
n (001) and (111) surfaces. For the case of island-relaxation without corne
r diffusion the asymptotic exponent is found to satisfy n similar or equal
to 1/4. However, when rapid corner-diffusion is allowed, the coarsening exp
onent is found to approach 1/3. An explanation for these results is present
ed in terms of the effects of corner diffusion on the surface current and m
ound morphology. [S0163-1829(99)51440-9].