Regularity results for solutions of nonlinear elliptic equations with L1,λL1,λ data

We consider the Dirichlet problem associated with equations whose prototype is −Δpu=fin Ω where Ω⊂RnΩ⊂Rn, n≥3n≥3, p∈[2,n[p∈[2,n[, −Δp is the pp-Laplacian operator and ff belongs to the Morrey space L1,λ(Ω)L1,λ(Ω) with λ∈]0,n−p]λ∈]0,n−p].Firstly, we prove that the gradient of the truncation Tj(u)Tj(u) belongs to Llocp,λ(Ω) for all j>0j>0 and, as a consequence, we establish regularity results in suitable weak Morrey spaces for uu and its gradient.