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: −∆u+u|Du|^2 =f or |Du|^2 − ∆u + u^θ = f, θ ∈ ]0, 1[, where the right-hand side f belongs to a suitable Morrey space, for instance to L^{1,λ}, 0 < λ ≤ N − 2, and we prove corresponding Morrey estimates for the gradient of a solution.