  We studied the asymptotic behavior of local solutions for strongly coupled
critical elliptic systems near an isolated singularity. For the dimension less
than or equal to five we prove that any singular solution is asymptotic to a
rotationally symmetric Fowler type solution. This result generalizes the
celebrated work due to Caffarelli, Gidas, and Spruck [1] who studied asymptotic
proprieties to the classic Yamabe equation. In addition, we generalize similar
results by Marques [11] for inhomogeneous context, that is, when the metric is
not necessarily conformally flat.
