Regularity results for solutions of nonlinear elliptic equations with [formula omitted] data

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We consider the Dirichlet problem associated with equations whose prototype is − Δ p u = f in Ω where Ω ⊂ R n , n ≥ 3 , p ∈ [ 2 , n [ , − Δ p is the p -Laplacian operator and f belongs to the Morrey space L 1 , λ ( Ω ) with λ ∈ ] 0 , n − p ] . Firstly, we prove that the gradient of the truncation T j ( u ) belongs to L loc p , λ ( Ω ) for all j > 0 and, as a consequence, we establish regularity results in suitable weak Morrey spaces for u and its gradient.