Entropy and Renormalized Solutions for a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces

In this paper, we establish the equivalence of entropy and renormalized solutions of secondorder elliptic equations with nonlinearities defined by the Musielak–Orlicz functions and the right-hand side from the space L₁(Ω). In nonreflexive Musielak–Orlicz–Sobolev spaces, we prove the existence and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with a Lipschitz boundary.