By means of a coarse-graining technique, we derive the effective anchoring
energy of a nematic liquid crystal in contact with a macroscopically corrug
ated surface imposing a weak degenerate planar anchoring. For coarse-graine
d nematic director's profiles that vary only in the direction perpendicular
to the average surface's plane, our results generalize those already known
by including the anisotropy of the elastic constants. In the general case,
on the contrary, we show that extra surface gradient terms appear that gen
erally are not negligible. [S1063-651X(99)14908-0].