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

Abstract

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.