Regularity results for solutions of nonlinear elliptic equations with image data Original Research Article

We consider the Dirichlet problem associated with equations whose prototype is View the MathML source−Δpu=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 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 View the MathML sourceLlocp,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.