Abstract
We consider second-order elliptic equations with nonlinearities determined by Musielak–Orlicz functions and with right-hand side in the space. In the Musielak–Orlicz–Sobolev spaces, we establish some properties and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with Lipschitz boundary. In addition, the equivalence and sign-definiteness of the entropy and renormalized solutions is proved.
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