LAUSR

Abstract We are concerned with positive solutions of the fractional elliptic system ( E ) { ( − Δ ) s u = f ( v ) in  Ω , ( − Δ ) s v = g ( u ) in  Ω , where Ω is an arbitrary domain in R N ( N > 2 s ), s ∈ ( 1 2 , 1 ) and f , g ∈ C l o c β ( R ) , for some β ∈ ( 0 , 1 ) . We establish universal a priori estimate for positive solutions of (E) . Then for C 2 bounded domain Ω, we prove the existence of positive solutions of (E) with prescribed boundary value u = μ and v = ν where μ , ν are positive bounded measure on ∂Ω and discuss regularity property of the solutions.