Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces

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Gossez's approximation theorems in Musielak–Orlicz–Sobolev spaces (2017, unknown): “[18, 20]) to provide a modular density result not for W 0 LM (Ω), but for V m 0 LM (Ω) = {u ∈ W 1,1 0 (Ω) ∩W (Ω) : Du ∈ LM (Ω)}, where W 1,1 0 (Ω) is defined as a closure of C ∞ 0 (Ω) in W (1,1)(Ω)–norm.”
Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space (2017, methodology): “Renormalized solutions to elliptic problems in Orlicz spaces are explored in [1, 2, 6], while in Musielak-Orlicz spaces in [24, 25].”
Hölder regularity of quasiminimizers under generalized growth conditions (2017, background): “In addition to being a natural generalization which covers results from both variable exponent and Orlicz spaces, the study of nonstandard growth problems can be motivated by applications to image processing [1, 6, 21], fluid dynamics [40, 41] and differential equations [2, 14, 17, 18, 37, 38] The s”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “For the existence results for elliptic problems with nonstandard growth and data below duality we refer to [7, 26, 81, 92, 112, 113, 117, 141, 147].”
Renormalized solutions to nonlinear parabolic problems in generalized Musielak–Orlicz spaces (2015, methodology): “In [28] we have studied the existence and uniqueness of renormalized solutions of the corresponding elliptic problem to (P, f, b0).”