Generalized Orlicz spaces and related PDE

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Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space (2017, methodology): “Meanwhile in [27, 28], the proposed condition yields φ(x, b|ξ|) ≤ φ(y, |ξ|) when φ(y, |ξ|) ∈ [1, |x − y|−n], which does not imply (6) directly.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “In [92, 117, 147] isotropic, separable and reflexive Musielak-Orlicz spaces are employed, [81] studies separable, but not reflexive Musielak-Orlicz spaces, while in anisotropic and non-reflexive Musielak-Orlicz spaces in [106, 112, 113].”
New martingale inequalities and applications to Fourier analysis (2018, background): “The Musielak–Orlicz spaces not only have their own interest, but they are also very useful in partial differential equations [2, 5, 28, 26], in calculus of variations [13], in image restoration [27, 43] and in fluid dynamics [73, 51].”
Extrapolation and interpolation in generalized Orlicz spaces (2018, methodology): “For more information on these spaces, see [31].”