Renormalized solutions to nonlinear problems in the generalized Musielak-Orlicz spaces

I will discuss the recent results on exitence of renormalized solutions to strongly nonlinear problems with L^1-data. Unlike other studies, we are able to consider the minimal growth conditions (prescribed by any anisotropic and nonhomogeneous Orlicz function), imposing instead constraints on the regularity of the modular function.
This is the joint work with Anna Zatorska-Goldstein and Piotr Gwiazda.