Inserted: 12 nov 2012
Last Updated: 5 apr 2013
Journal: Journal of Differential Equations
We study the symmetry properties for solutions of elliptic systems involving the fractional Laplacian. The study of this kind of system is made via a careful analysis of the~$\alpha$-harmonic extension in the half-space. We prove some Poincar\'e-type formulas, from which we derive a symmetry result both for stable and for monotone solutions.