Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and L1 terms

In this paper we deal with the following boundary value problem{−Δpu+g(u)|∇u|p=h(u)fin Ω,u≥0in Ω,u=0on ∂Ω, in a domain Ω⊂RN (N≥2), where 1≤p<N, g is a positive and continuous function on [0,∞), and h is a continuous function on [0,∞) (possibly blowing up at the origin). We show how the presence of regularizing terms h and g allows to prove existence of finite energy solutions for nonnegative data f only belonging to L1(Ω).