On W1,q(⋅)-estimates for elliptic equations of p(x)-Laplacian type

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Maximal regularity for local minimizers of non-autonomous functionals (2019, unknown): “r = 0 =⇒ u∈ Cα for any α∈ (0,1), ωp(r) . rβ for some β>0 =⇒ u∈ C1,α for some α∈ (0,1). (2.2) For these results, we refer to the series of papers of Acerbi, Coscia and Mingione [2, 3, 28], see also [4, 18, 41, 42]. For type III, i.e. ϕ(x,t) = tp+a(x)tq, suppose a∈ C0,β for some β∈ (0,1]. Then (2.3”
Existence and multiplicity results for a newp(x)-Kirchhoff problem (2019, background): “n a great deal of workdone on problem(1.1), especially concerningthe existence, multiplicity,uniquenessand regularityof solutions. Some important and interesting results can be found, for example, in [4, 5, 3, 2, 7, 10, 8, 11, 12, 13, 15, 18, 21, 19, 22, 23, 24, 25, 29, 30, 31, 32, 33, 40] and refer”