Gradient estimate for solutions of nonlinear singular elliptic equations below the duality exponent

In this paper, we study the homogeneous Dirichlet problem for an elliptic equation whose simplest model is − Δ u + M | D u | 2u θ= f in Ω ,where Ω ⊂ R N , N ≥3 is an open bounded set, θ ∈]0,1[, and f belongs to a suitable Morrey space. We will show that the Morrey property of the datum is transmitted to the gradient of a solution.