# A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian

created by pinamonti on 12 Nov 2012
modified on 05 Apr 2013

[BibTeX]

Accepted Paper

Inserted: 12 nov 2012
Last Updated: 5 apr 2013

Journal: Journal of Differential Equations
Year: 2013

Abstract:

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.