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Local gradient estimates for the p(x)-Laplacian elliptic equations
In this paper we give a new and direct proof of local L q estimates for the nonhomogeneous p(x) -Laplacian elliptic equation under some proper conditions on p(x) > 1 .We prove that |f| p(x) ∈ L q loc =⇒ |∇u| p(x) ∈ L q loc for any q 1 …