Qualitative analysis of positive singular solutions for a critical elliptic system in a punctured ball

We study qualitative properties of positive singular solutions to a weakly coupled elliptic system with critical exponents in a punctured ball.

We give a sharp criterion on the removability of the isolated singularity.

We also prove the nonexistence of positive solutions with one component bounded near the singularity and the other component unbounded near the singularity.

Asymptotic symmetry and sharp pointwise estimates are also proved for singular solutions.

These generalizes some classical results of (Caffarelli, Gidas and Spruck, Comm.

Pure Appl.

Math, 1989) to the weakly coupled system.