Nonlinear elliptic equations with lower order terms and image-data Original Research Article

We consider the Dirichlet problem associated to equations whose prototype is View the MathML source−Δpu+u|Du|p=fin Ω Turn MathJax on where Ω⊂RnΩ⊂Rn, n≥3n≥3, p∈[2,n[p∈[2,n[, View the MathML source−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 View the MathML sourceLlocp,λ(Ω).