We study the symmetry properties for solutions of elliptic systems of the type (-\Delta)^{ s_1} u = F_1(u, v), (-\Delta)^{ s_2} v= F_2(u, v), where $F\in C^{ 1,1}_{ loc}(\R^2)$, $s_1,s_2\in (0,1)$ and the operator $(-\Delta)^s$ is the so-called fractional Laplacian. We obtain some Poincar\'e-type formulas for the $\alpha$-harmonic extension in the half-space, that we use to prove a symmetry result both for stable and for monotone solutions.
Categories: math.AP