Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity

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Gradient estimates for elliptic equations with Lp(·)logL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p(\cdot )}\ (2016, methodology): “2 looks quite similar to the ones of results for p(·) Laplace type equations, see [2,5].”
Regularity for general functionals with double phase (2017, result): “3), while further results in this direction can be for instance found in [2, 3, 4, 8, 11, 9, 12, 13, 14, 20, 47, 48, 49, 52]; see also the work of Ragusa & Tachikawa for partial regularity [50, 51, 52].”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “3] and related references, and [40] for a global result.”
Lipschitz Bounds and Nonautonomous Integrals (2020, background): “em in (1.5), Dc∈ Lnimplies that c(·) ∈ VMO, the space of functions with vanishing mean oscillations [64]. At this point, Du∈ Lp loc(Ω), for everyp≥ 1, followsfrom the standardtheory (see for instance [9,35]). In fact, we provide the ﬁrst Calderón-Zygmund type estimates in problems with nonpolynomial”