Existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and L1-data

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Renormalized solutions for a nonlinear parabolic equation with variable exponents and l(1)-data (2010, background): “In particular, it follows from the results of [33] that, for all f ∈ L1(Ω), λ > 0, there exists a unique renormalized solution u : Ω → R of the problem (E)λ( f ) { u − λdiv(|∇u|p(x)−2∇u) = f in Ω, u = 0 on ∂Ω, (50) i.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Note that [24, 195] concern isotropic variable exponent spaces, while [22, 23, 141] the anisotropic”
Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces (2012, methodology): “Using the same arguments as in [43], i.”
Renormalized solutions to nonlinear parabolic problems in generalized Musielak–Orlicz spaces (2015, background): “Thanks to the assumption (i), the spaces are reflexive and separable what significantly facilitates the considerations (see [7, 46]) since classical monotonicity methods are applicable.”
Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space (2017, background): “Their generalisations to the variable exponent setting can be find in [3, 4, 42].”