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

Abstract

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: −Δu+u|Du|2=for −Δu+|Du|2uθ=f,θ∈]0,1[,where the right-hand side f belongs to a suitable Morrey space, for instance to L1,λ, 0<λ≤N−2, and we prove corresponding Morrey estimates for the gradient of a solution.