The quasi-minimizer of integral functionals with m ( x ) growth conditions

By Xianling Fan, Dun Zhao. 2000

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The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values (2006, background): “Local minimizers and quasiminimizers have been studied also by Fan and Zhao [14, 15 ].”
On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators (2005, unknown): “11 , Fan and Zhang 12 , Fan and Zhao 13–15 , Kovacik 16 , Marcellini 17 , Zhikov 18 and references therein.”
Overview of differential equations with non-standard growth (2010, methodology): “Basic results on the Cα continuity of solutions for some α ∈ (0, 1) were derived by Fan and Zhao [97, 98, 99].”
Existence of positive solutions for a class of p(x)-Laplacian systems ✩ (2007, unknown): “Many results have been obtained on this kind of problems, for example [1–3,6–13,16,18].”
Quasilinear elliptic problems with nonstandard growth. (2011, background): “Samko [16, 17, 18] working based on earlier Russian work (Sharapudinov [19] and Zhikov [20]), Fan and collaborators [5, 6, 7, 8] drawing inspiration from the study of differential equations(e.”
Global C1,α regularity for variable exponent elliptic equations in divergence form (2007, background): “According to [9,10], we have the following results on the Hölder continuity of the bounded generalized solutions.”