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We investigate qualitative properties of positive singular solutions of someelliptic systems in bounded and unbounded domains. We deduce symmetry andmonotonicity properties via the moving plane procedure. Moreover, in theunbounded case, we study some cooperative elliptic systems involving criticalnonlinearities in $\mathbb{R}^n$.

Symmetry and monotonicity properties of singular solutions to some cooperative semilinear elliptic systems involving critical nonlinearities