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We studied the asymptotic behavior of local solutions for strongly coupledcritical elliptic systems near an isolated singularity. For the dimension lessthan or equal to five we prove that any singular solution is asymptotic to arotationally symmetric Fowler type solution. This result generalizes thecelebrated work due to Caffarelli, Gidas, and Spruck [1] who studied asymptoticproprieties to the classic Yamabe equation. In addition, we generalize similarresults by Marques [11] for inhomogeneous context, that is, when the metric isnot necessarily conformally flat.

Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent