Renormalized solutions to nonlinear parabolic problems in generalized Musielak–Orlicz spaces

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Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space (2017, unknown): “We follow the ideas of [26] involving the Chacon Biting Lemma and the Young measure approach to show that for s→ ∞ it holds that As,l+1 · ∇Tl+1(us) −⇀ A(x,∇Tl+1(u)) · ∇Tl+1(u) weakly in L(1)(Ω).”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “An interesting idea of proofs in the parabolic case in [47, 48, 114] is that the notion of renormalized solution is employed to get weak solution to truncated and regularized problem.”
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”