Global gradient estimates for general nonlinear elliptic measure data problems with Orlicz growth

We provide an optimal global Calderon-Zygmund theory for gradients of SOLAs to general nonlinear elliptic equations -div 31(x, u, Du) = mu whose principle part depends on the solution itself and right-hand data mu is a signed Radon measure. The associated nonlinearity 31 is assumed to satisfy the (delta,R-0)-BMO condition in x, local uniform continuity in u, and Orlicz growth condition in Du, while the boundary of underlying domain is assumed to be Reifenberg flat. This is achieved by employing a perturbation method together with developing a one-parameter technique and by applying the maximal function free technique. (c) 2023 Elsevier Inc. All rights reserved.