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

We are concerned with positive solutions of the fractional elliptic system { (-Delta)(s)u = f(v) in Omega, 1 (-Delta)(s)v = g(u) in Omega, (E) where Omega is an arbitrary domain in R-N (N > 2s), s is an element of (-1/2-, 1) and f, g Omega C-loc(beta)(R), for some beta is an element of (0, 1). We establish universal a priori estimate for positive solutions of (E). Then for C-2 bounded domain Omega, we prove the existence of positive solutions of (E) with prescribed boundary value u = mu and v = v where mu, v are positive bounded measure on partial derivative Omega and discuss regularity property of the solutions. (C) 2019 Elsevier Inc. All rights reserved.