(untitled) (Journal of Mathematical Study, 2021)
In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x,Du)+F(u)) ∋ f in Ω where f ∈ L^1(Ω). A vector field a(.,.) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general L^1-data.