Regularizing effect for some p-Laplacian systems

We study existence and regularity of weak solutions for the following p-Laplacian system −Δpu+Aφθ+1|u|r−2u=f,u∈W01,p(Ω),−Δpφ=|u|rφθ,φ∈W01,p(Ω),where Ω is an open bounded subset of RN(N≥2), Δpv≔div(|∇v|p−2∇v) is the p-Laplacian operator, for 10, r>1, 0≤