Morrey estimates for some classes of elliptic equations with a lower order term

We will browse a series of results on elliptic equations and systems, with particular nonlinear lower order terms and measure right-hand side, obtained in the last years in the papers (Cirmi and Leonardi, 2014; Cianci et al., 2017; Cirmi et al., 2014, 2017, 2018). Namely we take into account equations whose prototypes are: -Delta u + u vertical bar Du vertical bar(2) = f or -Delta u + vertical bar Du vertical bar(2)/u(theta) = f, theta is an element of]0, 1[, where the right-hand side f belongs to a suitable Morrey space, for instance to L-1,L-lambda, 0 < lambda <= N - 2, and we prove corresponding Morrey estimates for the gradient of a solution. (C) 2018 Elsevier Ltd. All rights reserved.