Nonlinear elliptic equations with lower order terms and L1,λL1,λ-data

We consider the Dirichlet problem associated to equations whose prototype is −Δpu+u|Du|p=fin Ω where Ω⊂RnΩ⊂Rn, n≥3n≥3, p∈[2,n[p∈[2,n[, −Δp is the pp-Laplacian operator, ff belongs to the Morrey space L1,λ(Ω)L1,λ(Ω) with λ∈[0,n[λ∈[0,n[. We prove that DuDu belongs to the space Llocp,λ(Ω).