Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth

We prove a global Morrey regularity for the gradients of weak solution to nonlinear elliptic equations under controlled growth with partial BMO nonlinearities in x-variables over Reifenberg flat domains. We mainly suppose that the principal nonlinearity is merely measurable in one variable and has a small BMO seminorm in the remaining variables; while the lower order terms are subjected to the so-called controlled growth of the gradients, and the boundary of underlying domain is sufficiently flat in the sense of Reifenberg. (C) 2018 Elsevier Ltd. All rights reserved.