Nonlinear fractional elliptic systems with boundary measure data: Existence and a priori estimates

Abstract

We are concerned with positive solutions of the fractional elliptic system () where Ω is an arbitrary domain in (), and , for some . We establish universal a priori estimate for positive solutions of (E). Then for bounded domain Ω, we prove the existence of positive solutions of (E) with prescribed boundary value and where are positive bounded measure on ∂Ω and discuss regularity property of the solutions.